Discovering the Shape of Spacetime from the Big Bang: A Scientific Exploration

[Ken G]

As I said, I'm an agnostic about the perfect spatial flatness issue. Perfect absolute spatial flatness (on cosmic scales) has not been ruled out, nor has it been proven.

I would go further-- I would say that "perfect flatness" is actually a meaningless scientific concept in the first place. We don't ascertain perfection in science, we simply make models. When we have some evidence that requires we put in spatial curvature, we will, but it is quite likely that we will never have any evidence to put that into our models-- so our models will probably always be flat. That will never tell us if the universe is actually perfectly flat, nor does science have any business even asking that question (because it cannot be parlayed into any testable hypothesis). All we can say is that expansion, and the cosmological principle, are issues that are completely independent of the issue of spatial curvature. That is why the balloon analogy is not really a description of the cosmological principle, it is merely one situation in which the cosmological principle could apply. One should not mistake that for a model of our universe-- there is no reason to model the universe as having any spatial curvature, and no consensus model does.

The latest NASA report I recall on that gave a 95% confidence interval that included zero and plenty of scope on both sides of zero: a possibility of either positive or negative overall curvature.

Exactly, so no model of the universe would involve spatial curvature, it's a simple matter of Occam's Razor. But even if we did someday have a finite curvature observation, it would not require what we extrapolate that measurement to beyond what we can see, any more than we would extrapolate the preponderance of matter over antimatter to realms that we cannot see. We simply have no idea if unobservable realms are mainly matter or antimatter, and can easily come up with arguments why we could expect antimatter to dominate elsewhere. There's just no point in extrapolating, that's what I'm saying-- the point of science is to use models to make testable hypotheses, not to ask unanswerable questions.

Not sure what you mean by "current best models" being flat. As I recall the WMAP 5 year report used several models, including one which was spatially closed (but destined to expand indefinitely rather than re-collapse.) They fit several models to the data.

There is clearly a "best model" that is currently used as the consensus model, and it is flat. There's just no reason to use any other model at present-- this is even called "precision cosmology" because the model is more accurate than most other classes of astronomical models that get used routinely (like treating stars as spheres and so on). It doesn't mean there's no room to include non-flatness, it means there's no reason to include non-flatness, and no testable hypothesis motivated by a non-flat model has ever been borne out yet.

One can say that the data is consistent with overall spatial curvature being small. It could be zero, but we shouldn't pretend that we know that, when we actually do not.

Note that I never said we know the curvature is zero-- I said that the best model does not need, nor does it include, any curvature, and if inflation is true, then it never will. Science doesn't tell us if the curvature is zero, it tells us if we need to include non-flatness in our model.

 

[AlbertE]

How can it be flat - when its clearly not flat? This is getting strange.

I sometimes wonder whether science has somehow lost the plot. Then again - maybe I lost the plot - then again - maybe I never had the plot in the first place.

I see what I see.

I see matter forming tiny structures called galaxies, billions of them, and they sit in space - which has no air so we call it a vacuum because we do have air down here and it puts pressure on us.

These tiny galaxies appear to be moving away from each other in 3D space, there is no flatness that I can see.

I thought science was all about (or at least partly about) proving by observation.

The universe is not flat - at all.

 

[twofish-quant]

This all might seem like a fairly moot issue, but in fact it has a lot to do with how we teach cosmology.

Agreed.

But over and over, the search for any spatial curvature has failed to find any (at cosmological scales), so I would argue that it is high time we simply start building in a spatially flat universe right into how we conceive and teach cosmology.

That's wrong.

1) You need to look at curvature to show that it doesn't exist.
2) The inflationary models of the universe predicts small but non-zero curvature.
3) It's a bad idea to remove essential physics for pedagological purposes.

All that overhead away when we get to the actual observations and the current best models-- which are both flat!

That's false, if the universe were perfectly flat, then we'd run into fine tuning problems with inflation.

One issue is topology. You can make a sphere *look* flat by expanding it, but a big sphere is still topologically a sphere.

The flatness of space on cosmological scales is about as important of a cosmological principle as there is.

Strongly disagree.

 

[twofish-quant]

I would go further-- I would say that "perfect flatness" is actually a meaningless scientific concept in the first place.

Strongly. There is a term in the FLRW that jumps discontinuously between k=-1, k=0, and k=+1. Perfect flatness is k=0.

When we have some evidence that requires we put in spatial curvature, we will, but it is quite likely that we will never have any evidence to put that into our models-- so our models will probably always be flat.

This is false. If k=0, then certain numbers have to take exact values. If those values are even slightly off, then k=-1, or k=1.

One should not mistake that for a model of our universe-- there is no reason to model the universe as having any spatial curvature, and no consensus model does.

Again this is false. Lambda-CDM allows you to calculate the spatial curvature given input parameters. It so happens that the observations are consistent with k=0, but they are also consistent with small positive or negative curvature.

The model of gravity that we use *depends* on spatial curvature to exist. If you *impose* zero curvature, then you are using something other than GR to do your calculations. Inventing gravity models out of thin air, is not advisable.

The fact that the world looks flat if you look at distances of 500 feet, doesn't mean that it is, and you can take some precision measurements to show curvature.

We simply have no idea if unobservable realms are mainly matter or antimatter, and can easily come up with arguments why we could expect antimatter to dominate elsewhere.

It's testable. We can exclude anti-mater within a radius of "x light years" since that would change the CMB.

There's just no point in extrapolating, that's what I'm saying-- the point of science is to use models to make testable hypotheses, not to ask unanswerable questions.

You don't know that the questions are unanswerable unless you try to answer them.

There is clearly a "best model" that is currently used as the consensus model, and it is flat.

No it's not. It has curvature < N, where N is a number less than observation, but curvature < N is not the same as N=0.

Also, people are not inclined to argue that if curvature < N means N=0. People were making similar arguments in the 1970's and 1980's about the matter content of the universe. The observations as of 1985 were consistent with a flat universe that consistent only of dark matter. It turns out that model was wrong.

It doesn't mean there's no room to include non-flatness, it means there's no reason to include non-flatness, and no testable hypothesis motivated by a non-flat model has ever been borne out yet.

Non-flatness is not excluded by current observations.

Note that I never said we know the curvature is zero-- I said that the best model does not need, nor does it include, any curvature, and if inflation is true, then it never will.

That's false. If inflation is true than the amount of curvature is small but non-zero. The amount of non-zeroness can rule out different inflation models.

If the curvature is in fact *exactly* zero, that rules out inflationary explanations for flatness. If the curvature is *exactly* zero then it must have been that way before inflation which would tell us something really important about quantum gravity.

Science doesn't tell us if the curvature is zero, it tells us if we need to include non-flatness in our model.

Theory tells us that if curvature is zero, then we live in a very weird universe with a very weird coincidence. Now if the curvature is merely "small" then that coincidence disappears.

 

[twofish-quant]

As I said, I'm an agnostic about the perfect spatial flatness issue. Perfect absolute spatial flatness (on cosmic scales) has not been ruled out, nor has it been proven.

Same here. I'm very strongly opposed to removing flatness from cosmological models unless there is a strong theoretical or observations reason to do so, because having a cosmological model that is perfect flat introduces a lot of "fine tuning" problems.

One can say that the data is consistent with overall spatial curvature being small. It could be zero, but we shouldn't pretend that we know that, when we actually do not.

Especially when we've been burned before. The cosmological observations circa 1985 were consistent with zero dark energy and baryon/dark matter masses creating a flat universe.

Yup, and if we did have any reason to think that it is exactly zero, then it would create lots of theoretical issues. Simple inflation would no longer work as an solution to the flatness problem. There are forms of inflation that would work as solutions. Conversely if we beat down the error bars and find that the universe is almost flat, that kills several classes of models.

 

[Ken G]

That's wrong.

1) You need to look at curvature to show that it doesn't exist.

Huh? Do I need to look at unicorns to show they don't exist? That's not how it works in science. In science, all claims of existence require evidence, it's just that simple. Are you as opposed to "eliminating unicorns from science" as you are to "eliminating curvature from our models"? General relativity allows for unicorns just as easily as it allows for curvature or for a cosmological constant, we don't include things in our models just because our theories allow for them to be there.

2) The inflationary models of the universe predicts small but non-zero curvature.

No that is not true, inflationary models predict only one thing: curvature will never be observable. That's all they predict.

3) It's a bad idea to remove essential physics for pedagological purposes.

You have not demonstrated that curvature is essential physics. Indeed, that is exactly why the current best model involves no spatial curvature at all. Indeed, as I said, the absence of spatial curvature in our models is clearly one of their very most important elements, it is second in importance only to the cosmological principle itself. And by the way, you should note that GR also allows for the cosmological principle to be "eliminated" too, are you against eliminating deviations from the cosmological principle from our cosmological models too?

So here's my question to you: why should we include deviations from flatness in our models, but not deviations from the cosmological principle? Please note that I never said anything like we know we cannot have non-flatness, any more than I would say we must have the cosmological principle-- what I have said is that the way science works is, we only put things in our models that we have evidence to put in there, and we always seek the simplest models that work. Flatness is no different.

That's false, if the universe were perfectly flat, then we'd run into fine tuning problems with inflation.

I think what you mean here is that one of the reasons we like inflation is that it "explains" flatness. But we don't know if we need to explain flatness, any more than we know if we need to explain quantum mechanics. The problem of "fine tuning" is one of the more bogus "problems" in physics, it has never been clear if that issue is science at all (witness all the questionable arguments around the anthropic principle and the "multiverse", questionable science at best). I think all these "fine-tuning" issues stem from a basic error in characterizing what science is-- science does not need to know, nor does it even get to know, if the universe is exactly flat or not, it merely needs to make good models, and understand why the models are good. Flatness is a good model in any universe with inflation, regardless of what the curvature "actually is" (if any such concept is even scientifically meaningful), that is absolutely all that can be said without leaving the building of what science is.

One issue is topology. You can make a sphere *look* flat by expanding it, but a big sphere is still topologically a sphere.

And a big saddle is still topologically a saddle, and a big plane is still topologically a flat plane. So what? None of that tells us anything about our universe, nor does our best model bother with it. What testable hypothesis are you talking about? None, so it's "not even wrong."

 

[twofish-quant]

Huh? Do I need to look at unicorns to show they don't exist?

We aren't talking about unicorns.

Curved space-time exists. There are lots of tests of GR that show this. The question is whether or not the large scale universe is curved, and that's an observational question and an open one.

It turns out that you *can* do a lot of cosmology using flat-space time, and Newtonian physics as a model of the universe. The trouble with this model is that it requires that the speed of light is infinite, and once you have a finite speed of light, then it becomes inconsistent.

General relativity allows for unicorns just as easily as it allows for curvature or for a cosmological constant, we don't include things in our models just because our theories allow for them to be there.

We include them because our theories *require* for them to be there.

No that is not true, inflationary models predict only one thing: curvature will never be observable.

Citation?

http://arxiv.org/abs/1203.6876
What can the observation of nonzero curvature tell us?

Alan Guth disagrees, and I can't find any statement from any standard reference text that says that inflation says that we will never observe curvature.

We resolve this point, and everything else gets resolved.

And by the way, you should note that GR also allows for the cosmological principle to be "eliminated" too, are you against eliminating deviations from the cosmological principle from our cosmological models too?

I'm a theorist. We remove assumptions, and see what happens. It turns out that you can't remove anisotropy and homogenity without running into problems with information traveling faster than light. It also turns out that you run into similar problems if you assume that space time curvature is zero in the presence of gravity.

So here's my question to you: why should we include deviations from flatness in our models, but not deviations from the cosmological principle?

Because it makes the math easier and because you can assuming isotropy/homogenity self-consistently whereas you can't remove curvature without getting a model that is inconsistent with itself.

Also, the "zero-th order" cosmological model assumes a smooth universe. LCDM is a "first-order" model because it includes density perturbations.

"Easy math" is an important aspect of a model, since a model that you can't make calculations from is useless. Also consistency with other physical principles is important. One reason we don't put large scale anisotropy in our cosmological models is that any large scale anisotropy will involve sending information faster than light, which is a bad thing. Conversely, one problem with models of the universe in which you force flatness is that they require FTL information exchange.

Please note that I never said anything like we know we cannot have non-flatness, any more than I would say we must have the cosmological principle-- what I have said is that the way science works is, we only put things in our models that we have evidence to put in there, and we always seek the simplest models that work.

Strongly disagree. We put stuff that we don't know is there in our models so that we can do calculations to show that it's not there.

Also models have to have constraints. Any model that is non-self consistent is going to have problems. Any model that requires fine-tuning is a problem

But we don't know if we need to explain flatness, any more than we know if we need to explain quantum mechanics. The problem of "fine tuning" is one of the more bogus "problems" in physics, it has never been clear if that issue is science at all (witness all the questionable arguments around the anthropic principle and the "multiverse", questionable science at best).

Disagree. There are lots of heuristics in science. Occam's razor is one. "Avoid weird coincidences" is another.

I think all these "fine-tuning" issues stem from a basic error in characterizing what science is-- science does not need to know, nor does it even get to know, if the universe is exactly flat or not, it merely needs to make good models, and understand why the models are good.

Any model that requires "fine tuning" is a bad model.

A lot of science involves heuristics. Historically, any time you have a "weird coincidence" then that's a sign that you should look at the weird conincidence very carefully and see why it's there, because you'll likely discover something.

Flatness is a good model in any universe with inflation, regardless of what the curvature "actually is" (if any such concept is even scientifically meaningful), that is absolutely all that can be said without leaving the building of what science is. And a big saddle is still topologically a saddle, and a big plane is still topologically a flat plane. So what? None of that tells us anything about our universe, nor does our best model bother with it. What testable hypothesis are you talking about? None, so it's "not even wrong."

This is totally incorrect. Again see the Guth paper.

Also, when we say inflation tends to make the universe "flat" we aren't saying that it makes inflation undetectable.

The current thinking is that inflation is a product of the strong force separating itself from the other forces. Using our best understanding of grand unified theories, we can calculate curvature of the universe, and we get a number like curvature=10^100. The point of inflation was to provide a mechanism by which you can reduce curvature=10^100 to something of factor unity. So when someone says that inflation makes curvature "small", they are talking about 0<= curvature < 10.

A lot of this argument seems to be you thinking that inflation states that any curvature would be undetectable, and that's just not true. I've provided several citations in which people have stated otherwise, and I'd appreciate it if you could explain where you got the idea that inflation makes curvature undetectable.

 

[twofish-quant]

Huh? Do I need to look at unicorns to show they don't exist?

We aren't talking about unicorns.

Curved space-time exists. There are lots of tests of GR that show this. The question is whether or not the large scale universe is curved, and that's an observational question and an open one.

It turns out that you *can* do a lot of cosmology using flat-space time, and Newtonian physics as a model of the universe. The trouble with this model is that it requires that the speed of light is infinite, and once you have a finite speed of light, then it becomes inconsistent.

General relativity allows for unicorns just as easily as it allows for curvature or for a cosmological constant, we don't include things in our models just because our theories allow for them to be there.

We include them because our theories *require* for them to be there.

No that is not true, inflationary models predict only one thing: curvature will never be observable.

Citation?

http://arxiv.org/abs/1203.6876
What can the observation of nonzero curvature tell us?

Alan Guth disagrees, and I can't find any statement from any standard reference text that says that inflation says that we will never observe curvature.

We resolve this point, and everything else gets resolved.

And by the way, you should note that GR also allows for the cosmological principle to be "eliminated" too, are you against eliminating deviations from the cosmological principle from our cosmological models too?

I'm a theorist. We remove assumptions, and see what happens.

So here's my question to you: why should we include deviations from flatness in our models, but not deviations from the cosmological principle?

Because it makes the math easier and because you can assuming isotropy/homogenity self-consistently whereas you can't remove curvature without getting a model that is inconsistent with itself.

Also, the "zero-th order" cosmological model assumes a smooth universe. LCDM is a "first-order" model because it includes density perturbations.

"Easy math" is an important aspect of a model, since a model that you can't make calculations from is useless. Also consistency with other physical principles is important. One reason we don't put large scale anisotropy in our cosmological models is that any large scale anisotropy will involve sending information faster than light, which is a bad thing. Conversely, one problem with models of the universe in which you force flatness is that they require FTL information exchange.

Please note that I never said anything like we know we cannot have non-flatness, any more than I would say we must have the cosmological principle-- what I have said is that the way science works is, we only put things in our models that we have evidence to put in there, and we always seek the simplest models that work.

Strongly disagree. We put stuff that we don't know is there in our models so that we can do calculations to show that it's not there.

Also models have to have constraints. Any model that is non-self consistent is going to have problems. Any model that requires fine-tuning is a problem

But we don't know if we need to explain flatness, any more than we know if we need to explain quantum mechanics. The problem of "fine tuning" is one of the more bogus "problems" in physics, it has never been clear if that issue is science at all (witness all the questionable arguments around the anthropic principle and the "multiverse", questionable science at best).

Disagree. There are lots of heuristics in science. Occam's razor is one. "Avoid weird coincidences" is another.

I think all these "fine-tuning" issues stem from a basic error in characterizing what science is-- science does not need to know, nor does it even get to know, if the universe is exactly flat or not, it merely needs to make good models, and understand why the models are good.

Any model that requires "fine tuning" is a bad model.

A lot of science involves heuristics. Historically, any time you have a "weird coincidence" then that's a sign that you should look at the weird conincidence very carefully and see why it's there, because you'll likely discover something.

Flatness is a good model in any universe with inflation, regardless of what the curvature "actually is" (if any such concept is even scientifically meaningful), that is absolutely all that can be said without leaving the building of what science is. And a big saddle is still topologically a saddle, and a big plane is still topologically a flat plane. So what? None of that tells us anything about our universe, nor does our best model bother with it. What testable hypothesis are you talking about? None, so it's "not even wrong."

This is totally incorrect. Again see the Guth paper.

Also, when we say inflation tends to make the universe "flat" we aren't saying that it makes inflation undetectable.

The current thinking is that inflation is a product of the strong force separating itself from the other forces. Using our best understanding of grand unified theories, we can calculate curvature of the universe, and we get a number like curvature=10^100. The point of inflation was to provide a mechanism by which you can reduce curvature=10^100 to something of factor unity. So when someone says that inflation makes curvature "small", they are talking about 0<= curvature < 10.

A lot of this argument seems to be you thinking that inflation states that any curvature would be undetectable, and that's just not true. I've provided several citations in which people have stated otherwise, and I'd appreciate it if you could explain where you got the idea that inflation makes curvature undetectable.

 

[Ken G]

We aren't talking about unicorns.

Curved space-time exists.

So do strange animals just recently discovered. We are always finding out new things, always getting shocked about how much different things are from what we thought. None of that changes what science does-- science takes the current evidence and forms the best and simplest models that are consistent with it. When cosmologists do that, they model the universe as something flat and exhibiting a cosmological principle, i.e., they create an infinite model. That's just what they do, it's not a matter of opinion or debate. This is the model we have. Now, it might change, but it hasn't at the moment, and it never will if inflation happened.

Citation?

http://arxiv.org/abs/1203.6876
What can the observation of nonzero curvature tell us?

Alan Guth disagrees, and I can't find any statement from any standard reference text that says that inflation says that we will never observe curvature.

I should clarify-- I'm talking about standard inflation, not one of the trendy versions that multiverse folks have dreamed up! (Like "eternal inflation", for example, which in my view is pure philosophy masquerading as science. Yes, it is testable, but so are the gravitational fields of invisible unicorns-- the real issue is whether we have any reason to think we need to test for these things when we have zero evidence for them beyond some pipe dream that the universe can be better understood in a landscape of other universes.) The argument that standard inflation, in just one single universe (ours), would not allow any curvature to be detected is simply that inflation suffices to make the universe incredibly flat. Whatever curvature does exist then begins to grow exponentially after inflation ends, but the textbook numbers used to talk about inflation produce such staggering flatness that we are nowhere close to being able to see any curvature. The very fact that Guth is invoking anthropic arguments demonstrates my point-- the issue there is, you need to believe you have a vast number of different inflationary events in a vast number of universes to find even one in which the curvature would be detectable by us, and then you invoke anthropic arguments to claim that this is just the universe we would find ourselves in. So yes, if you are a fan of the idea that anthropic thinking should count as science, then you can argue that we can have "eternal inflation" and still see curvature (which is what Guth's paper is doing), but if you think anthropic thinking is not science (at best) or bunk (at worst), then you return to my claim that we will not see curvature if there is just one universe and it underwent one inflationary event. Guth's article does not refute it, indeed it supports it (that's the whole reason he is talking about "eternal inflation" in the first place).

Also, the "zero-th order" cosmological model assumes a smooth universe. LCDM is a "first-order" model because it includes density perturbations.

Sure, and the density perturbations appear against a background that is flat and has a cosmological principle, so is an infinite universe model. Maybe it could be argued that fluctuations must break that model up into pockets of open and closed universes on some huge scale, but I don't think the model constrains fluctuations on those scales, so as usual the model simply says nothing about such fluctuations, and does not make claims on a truth that science can never know because we cannot make testable hypotheses around it.

"Easy math" is an important aspect of a model, since a model that you can't make calculations from is useless. Also consistency with other physical principles is important. One reason we don't put large scale anisotropy in our cosmological models is that any large scale anisotropy will involve sending information faster than light, which is a bad thing. Conversely, one problem with models of the universe in which you force flatness is that they require FTL information exchange.

No, the current model is precisely such a model. I think you are missing that models are idealizations, they are not claims on reality. If someone models the gravity of the Earth by treating the Earth as a sphere, they are not actually claiming the Earth is a sphere, they are just doing physics. This is always what physics theory does, there are no exceptions. Physics theory makes idealizations, not claims on reality. And the idealization we use in cosmology is that of a flat and infinite universe, because we have no evidence of anything else, unlike models of a spherical Earth.

Any model that requires "fine tuning" is a bad model.

If you buy anthropic thinking, yes. However, if you don't, then you say this whole obsession with "fine tuning problems" is a complete red herring. Take "eternal inflation", again. This is a way to pack anthropic thinking into a timeline, instead of into a landscape of parallel universes. You say that the universe inflated over and over again, ad infinitum, slightly differently each time, and eventually you can get a really major difference (because you have forever to work with!). Then you can end up with a universe that is as fine-tuned as you like, and you don't have to call it fine tuning, because you first had all those zillions of universes that weren't. Has this really resolved the issue of fine tuning? It's a deep issue around what is an "explanation" in science, but it sticks in my craw to the point that I just say "who cares if the universe seems fine tuned, it is what it is." Embedding it in zillions of other universes we cannot observe seems like a very poor excuse for science to me, all in the name of not having "fine tuning." It's killing the patient to cure a cold!

A lot of science involves heuristics. Historically, any time you have a "weird coincidence" then that's a sign that you should look at the weird conincidence very carefully and see why it's there, because you'll likely discover something.

Sure, and in this case, the "weird coincidence" is that the universe is flat! The explanation is inflation, then it's no coincidence at all. What would really be weird is the detection of curvature, then you'd start worrying about things like eternal inflation to try to explain it, as Guth examines. But I say it is much more logical to conclude that, if we detect curvature, it is because inflation is wrong, not because we need eternal inflation and anthropic thinking.

This is totally incorrect. Again see the Guth paper.

Again, see my explanation of why Guth is invoking eternal inflation, and other equally bizarre modern variants. Some do indeed count those as testable hypotheses, just as string theory proponents bend way over backward to try to argue they generate testable hypotheses to. Unfortunately, it's just not convincing that these are legitimate scientific hypotheses. They are certainly nothing like "if the light bends more than you thought it would in the eclipse of 1919, general relativity is passing a test"!

The current thinking is that inflation is a product of the strong force separating itself from the other forces. Using our best understanding of grand unified theories, we can calculate curvature of the universe, and we get a number like curvature=10^100. The point of inflation was to provide a mechanism by which you can reduce curvature=10^100 to something of factor unity. So when someone says that inflation makes curvature "small", they are talking about 0<= curvature < 10.

No, if that were true, people would be absolutely shocked that the current cosmological models are flat. Why do you think they are not shocked at all, and most actually expected this? This is a very important question for you to ponder (it's because if the flatness is not nearly exactly 1, it has no business at all being some arbitrary but measurable difference from 1).

A lot of this argument seems to be you thinking that inflation states that any curvature would be undetectable, and that's just not true. I've provided several citations in which people have stated otherwise, and I'd appreciate it if you could explain where you got the idea that inflation makes curvature undetectable.

What you don't realize is that those citations are all referring to anthropic variants of inflation, and other bizarre versions, that are motivated by people who want to imagine our universe is selected from a vast number of unobservable ones. That's not what I mean by the inflationary universe, I'm talking about just one, because I believe science should deal with our own universe.

 

[twofish-quant]

When cosmologists do that, they model the universe as something flat and exhibiting a cosmological principle, i.e., they create an infinite model.

How many cosmologists do you know personally?

I can tell you that the cosmologists that I know (and some of them are on the WMAP team) simply don't do this.

The other thing is that it would help if you start adding citations for your assertions.

I should clarify-- I'm talking about standard inflation, not one of the trendy versions

There is no such thing as "standard inflation". What is known is that if you assume that the universe expands a lot during the GUT epoch, that lots of problems disappear. People have tried (and generally failed) to get more specific, so "inflation" is a general framework, and we don't have enough data yet to create a "standard" version.

The argument that standard inflation, in just one single universe (ours), would not allow any curvature to be detected is simply that inflation suffices to make the universe incredibly flat. Whatever curvature does exist then begins to grow exponentially after inflation ends, but the textbook numbers used to talk about inflation produce such staggering flatness that we are nowhere close to being able to see any curvature.

Can you cite the textbooks?

Also this is incorrect, because as of 1995, the best cosmological model was strongly negatively curved, and this wasn't taken as evidence against inflation.

And the idealization we use in cosmology is that of a flat and infinite universe, because we have no evidence of anything else, unlike models of a spherical Earth.

Who is "we".

Again, I don't want to go deep into philosophy because I think that your understanding of the current cosmological models is just factually incorrect. I've given you citations to explain why I think you are incorrect, and if you want to defend yourself, you'll need to point me to where you got your information from.

 

[bapowell]

I should clarify-- I'm talking about standard inflation, not one of the trendy versions that multiverse folks have dreamed up!

Note that arguably the simplest and one of the earlist models of inflation -- Linde's chaotic model -- generically leads to eternal inflation. So there is not such a clear dividing line between simple, as you say "standard" inflation models, and those that are eternal. In fact, inflation that is not eternal appears to be the exception.

Sure, and the density perturbations appear against a background that is flat and has a cosmological principle, so is an infinite universe model.

A flat universe doesn't need to be infinite, and I agree with twofish that the standard operational view of modern cosmology does not make an assumption of infinity. The flatness that is generally assumed is relevant to the observable universe, but of course inflationary cosmology says nothing of the global geometry of the universe.

If you buy anthropic thinking, yes.However, if you don't, then you say this whole obsession with "fine tuning problems" is a complete red herring

This response confuses me. If you buy anthropic reasoning, then fine-tuning isn't an issue at all. If you don't buy it -- if you believe that the incredible exactitude of and smallness of the cosmological constant (and other values) is to be fundamentally explained -- then fine tuning is *the* issue of contention.

Take "eternal inflation", again. This is a way to pack anthropic thinking into a timeline, instead of into a landscape of parallel universes. You say that the universe inflated over and over again, ad infinitum, slightly differently each time, and eventually you can get a really major difference (because you have forever to work with!).

This isn't the conception of eternal inflation that is generally accepted, at least in my experience. In chaotic inflation, you have regions of the universe that are always -- at this very moment -- undergoing inflation. It's not a series in time -- it's that whole regions of the universe are inflating across space simultaneously. As non-inflating volumes percolate out of this inflating background, you can possibly get different low energy physics.

Then you can end up with a universe that is as fine-tuned as you like, and you don't have to call it fine tuning, because you first had all those zillions of universes that weren't. Has this really resolved the issue of fine tuning?

This is anthropic reasoning precisely.

 

[Ken G]

How many cosmologists do you know personally?

I can tell you that the cosmologists that I know (and some of them are on the WMAP team) simply don't do this.

The other thing is that it would help if you start adding citations for your assertions.

Don't you read the journal articles about modern precision cosmology? The LCDM is a flat model of the universe. Yes, read the articles, would you like me to cite a random samping?

There is no such thing as "standard inflation".

That will certainly come as a surprise to the mainstream community that talks about standard inflation. I think what you really mean is that there is no precise model of inflation that could be considered the standard one, which is true, but nothing I've said depends on any specific model. Rather, it is the general, and yes standard, features of inflation that I am talking about. And I am certainly not talking about "eternal inflation", which is very clearly a fringe version of inflation, and one I would never mention in an astronomy classroom.

What is known is that if you assume that the universe expands a lot during the GUT epoch, that lots of problems disappear. People have tried (and generally failed) to get more specific, so "inflation" is a general framework, and we don't have enough data yet to create a "standard" version.

Yes, I know all that.

Also this is incorrect, because as of 1995, the best cosmological model was strongly negatively curved, and this wasn't taken as evidence against inflation.

I covered this in another thread, but I'll repeat it here. No working astronomers I knew at the time felt that model was complete, it was obviously wrong and everyone knew it.

 

[Ken G]

Note that arguably the simplest and one of the earlist models of inflation -- Linde's chaotic model -- generically leads to eternal inflation. So there is not such a clear dividing line between simple, as you say "standard" inflation models, and those that are eternal. In fact, inflation that is not eternal appears to be the exception.

You are talking about efforts to include inflation into a physical theory. No such working theory exists (by which I mean, is tested and makes predictions beyond what it is built to fit), so it doesn't matter what arbitrary attributes the toy attempts present-- there's no reason to place any confidence in them. I am talking about the general notion that our universe underwent a phase of extremely rapid expansion at some very early epoch when gravity separated from the other forces. This epoch is pre-physics, in the sense that it was a period before any successful physics theory we have today could possibly have applied.

Now, there are certainly brave souls who are wading into this morass, almost completely absent of any observational support or constraints, who are trying to create physical theories that will produce inflation and also some kind of testable predictions, despite the incredibly poor track record of pre-data efforts in the history of physics. Good luck to them, but they have not a single substantive success to point to to date, which is hardly surprising. In contrast, the basic idea that inflation occurred (what I referred to as the "standard inflation" model), has met with a great deal of success in helping us to understand observations. That's why it gets taught in classrooms, which distinguishes it from the highly speculative efforts to describe it in detail, which are all very much on the fringe of mainstream astronomy and will probably not be remembered until something much more successful comes along.

A flat universe doesn't need to be infinite, and I agree with twofish that the standard operational view of modern cosmology does not make an assumption of infinity.

Look more closely at what I have been saying. I have said that cosmology not only makes no claims on the infinity of the universe, we already know it never will. Instead, all it will ever do is create models, and those models will be projected onto what we can actually observe, and that will be used to test the model. The model is infinite, not the universe. We don't get to know if the universe is infinite or not, we already know this (because we already know we cannot see far enough to see if it is finite). I have said that the question "is the universe finite or infinite" is a fundamentally unscientific question because it can never be answered unless the answer is "finite", and we already know we cannot answer it that way.

The flatness that is generally assumed is relevant to the observable universe, but of course inflationary cosmology says nothing of the global geometry of the universe.

A point I have already made several times, although there are several threads on this and perhaps that wasn't clear in this particular thread.

This response confuses me. If you buy anthropic reasoning, then fine-tuning isn't an issue at all.

Yes, that was the point. I'm saying that you have a choice about what bothers you more: fine tuning, or anthropic reasoning. Which is a more bitter pill for science to swallow, given that we must choose? I'm saying there is no reason to be bothered by fine tuning, but there is every reason to be bothered by anthropic thinking: it isn't scientific. We don't actually know that there is anything unscientific about creating models that are finely tuned, it is more like a kind of religious objection. I say if the universe appears finely tuned, then that's what it appears to be, science studies the way things are and doesn't tell them they can't be that way. But that's exactly what the multiverse camp is doing, they have arbitrarily decided that if we study the universe that we can actually do science on, and it comes out seeming finely tuned, then there must be more universe out there that we can't do science on, but isn't finely tuned. A bad choice of a worse poison, I'm arguing.

If you don't buy it -- if you believe that the incredible exactitude of and smallness of the cosmological constant (and other values) is to be fundamentally explained -- then fine tuning is *the* issue of contention.

Yes, but it doesn't need to be-- there is nothing in the scientific method that says "if your theory seems finely tuned, but you can constrain it, you must embed it in a wider theory that is not finely tuned, but you cannot constrain." There just is no step like that in the scientific process, you just say that is how things are. Science has done that countless times in so many places. Why are there laws at all? Why is action minimized? Why are there symmetries, and why are they broken sometimes? The multiverse camp pretends that these are scientific questions, but they are not-- they are just not the questions that science gets to answer. The multiverse camp is essentially trying to erase the distinctions between physics and philosophy that have been hammered out over the last few millennia, distinctions that have been largely responsible for the rapid advances in empirical science.

This isn't the conception of eternal inflation that is generally accepted, at least in my experience. In chaotic inflation, you have regions of the universe that are always -- at this very moment -- undergoing inflation. It's not a series in time -- it's that whole regions of the universe are inflating across space simultaneously.

Yes, but the inflation continues everywhere, hence "eternal." It contrasts it from purely spatial versions of the "landscape." However, this is a minor issue-- the main objection holds either way, it is all about whether or not we think it is a good idea to imagine one is doing science on distributions, when one has observational access to only one member of the "distribution." I'm saying that's horrible science, though it is useful for obtaining a "warm fuzzy feeling" that everything makes sense in some particular philosophical world view. All those attributes show that it is a form of religion or philosophy, not empirical science.

This is anthropic reasoning precisely.

I know, that is why I was describing it as anthropic thinking. My issue is that it only "explains" in the way any untestable creation myth might, but it isn't science because it's too easy to build the multiverse any way we like, to fit any observation we need. Fine tuning is a far smaller issue than that.

 

[alt]

Howde all.

With reference to matter originating from the big bang. Nothing else. No multiverse, no pbranes - nothing. Just the Big Bang.

Ok - given that galaxies are moving away from each other - then there is an overall outer edge shape created by these galaxies.

Lets say now that you can hold this "shape" in your hand. What does it look like?

a) A donut?
b) A soccer ball?
c) A rugby ball/american football?
d) Saturn?
e) A spiral galaxy?
f) Science does not know?

Cheers all.

g) a fairy tale ?

https://www.physicsforums.com/showthread.php?t=543690

 

[PhanthomJay]

Howde all.

With reference to matter originating from the big bang. Nothing else. No multiverse, no pbranes - nothing. Just the Big Bang.

Ok - given that galaxies are moving away from each other - then there is an overall outer edge shape created by these galaxies.

Lets say now that you can hold this "shape" in your hand. What does it look like?

a) A donut?
b) A soccer ball?
c) A rugby ball/american football?
d) Saturn?
e) A spiral galaxy?
f) Science does not know?

Cheers all.

I don't think anyone listens to Hawking anymore. I guess his Physics has become controversial. For what it's worth, see his book that came out about 20 years ago. Universe in a Nutshell. The universe is pear shaped. I admire and respect the great Stephen Hawking.

 

[bapowell]

You are talking about efforts to include inflation into a physical theory.

No, I am not. I'm simply saying that if you take any inflation model -- effective or otherwise -- you tend to find regions of the potential that support eternal inflation. This is a completely phenomenological statement, that has nothing to do with any specific realization of inflation. Even the simplest generic scalar potentials tend to give you eternal inflation -- that's all I'm saying. I said this in response to your statement that you could apparently distinguish between "standard inflation" and "eternal inflation". As I've stated with the reasoning above, I don't believe that this is a useful operational distiniction.

The model is infinite, not the universe.

Why is the model necessarily infinite? I would instead say that the model doesn't say one way or the other.

I know, that is why I was describing it as anthropic thinking. My issue is that it only "explains" in the way any untestable creation myth might, but it isn't science because it's too easy to build the multiverse any way we like, to fit any observation we need. Fine tuning is a far smaller issue than that.

Certainly, and I'm not necessarily in disagreement with you here. I was just attempting to clarify the distinction you were making between what constituted fine tuning and what constituted anthropic reasoning. This seems cleared up now. But, I want to point out that if we are ever able to pin down the form of the inflaton potential reliably, and, say, discover that it is a polynomial, with minimal assumptions (namely that the universe is larger than our Hubble patch) we are innevitably led to accept an eternal picture of inflation. Granted, we are not observing other pocket universes, but the consistency of the theory would in this case strongly imply their existence. This kind of indirect evidence has its place in the scientific method.

 

[twofish-quant]

I am talking about the general notion that our universe underwent a phase of extremely rapid expansion at some very early epoch when gravity separated from the other forces.

Not necessarily true. For inflation to work it has occur for some time after gravity separates.

This epoch is pre-physics, in the sense that it was a period before any successful physics theory we have today could possibly have applied

That's false. Inflation occurs at grand unification energies, and while those are high they are still at the levels at which you can make testable predictions (i.e. proton decay). Also, inflation does make some testable (and verified) predictions about the spectrum of the CMB. During the inflationary period, quantum mechanics works the same way that it does now, which means that any "quantum noise" gets expanded into density fluctuations, and you can calculate the spectrum, and those are consistent with the CMB.

With inflation, we are at the edge of "known physics" but we aren't in the land of total speculation.

Now, there are certainly brave souls who are wading into this morass, almost completely absent of any observational support or constraints, who are trying to create physical theories that will produce inflation and also some kind of testable predictions, despite the incredibly poor track record of pre-data efforts in the history of physics.

We have a ton of data in the form of CMB temperature fluctuations. Those were generated by inflation. The other thing is that inflationary theories produce lots of testable predictions, which is why it's hard to come up with one that works.

Look more closely at what I have been saying. I have said that cosmology not only makes no claims on the infinity of the universe, we already know it never will.

And I'm saying that you are wrong. Unknown does not mean unknowable.

There are a set of possible observations that would indicate that the universe is finite and round. If we detect non-zero curvature and then if we pin down the amount of expansion from CMB, then we can show that the universe is finite and estimate it's diameter.

The model is infinite, not the universe. We don't get to know if the universe is infinite or not, we already know this (because we already know we cannot see far enough to see if it is finite).

The model has a parameter that you can set which gives you infinite or finite.

I have said that the question "is the universe finite or infinite" is a fundamentally unscientific question because it can never be answered unless the answer is "finite", and we already know we cannot answer it that way.

And that's a false statement. A small positive curvature is consistent with inflation and the current observational data. You keep making false statements about cosmology, such as the notion that inflation *requires* a non-zero curvature. I've already given you papers in which cosmologists have presented models of inflation that are work with small positive non-zero curvature, which you haven't refuted.

I don't know what to do. Your understanding of inflation is simply incorrect. There's nothing in inflation or current cosmology that *requires* a flat, infinite universe. Whether the universe if round or not is a purely observational issue.

Yes, that was the point. I'm saying that you have a choice about what bothers you more: fine tuning, or anthropic reasoning.

If I flip a coin that someone tells me is a fair coin fifty times, and it comes up heads, I'll look carefully at the coin. My guess will be that there is something odd about the coin rather than the idea that I'm extremely lucky.

One good thing about inflation is that it killed several anthropic arguments.

We don't actually know that there is anything unscientific about creating models that are finely tuned, it is more like a kind of religious objection.

It's a heuristic. If I flip a coin fifty times, and it comes up heads, I'm going to look carefully at the coin to see why. There's nothing "religious" about this.

One other heuristic is avoid philosophy whenever possible.

It's possible that we get into weird philosophical issues once we go pre-inflation, but with inflation there is enough data that we can avoid those issues.

There's nothing in inflation or current cosmology that *requires* a flat, infinite universe. Whether the universe if round or not is a purely observational issue. We take lots of measurements and see what happens.

You are getting yourself into unnecessarily philosophical issues, because your understanding of the assumptions of current cosmology and of inflation is incorrect.

 

[Ken G]

No, I am not. I'm simply saying that if you take any inflation model -- effective or otherwise -- you tend to find regions of the potential that support eternal inflation.

I can't see how you can claim that without some physical basis for the cause of the inflation. If you simply assert that inflation occurred early in our universe, that is a statement that has nothing to do with eternal inflation. If you want to support that statement with some kind of physical theory, then you need to be able to say what observational tests that theory has satisfied, and there is a very long and exhaustive process that goes into gaining confidence in any such attempt. That currently just does not exist, so for the mainstream, inflation is just a statement of a phenomenon, not a theory, and no claims can be made on how likely or often it "should" occur.

This is a completely phenomenological statement, that has nothing to do with any specific realization of inflation.

How can you say that? The phenomenon is inflation, period. Saying it "should" happen eternally is not a phenomenological statement, it is a claim on some theory that has passed no tests other than what it was specifically built to pass (if that).

Even the simplest generic scalar potentials tend to give you eternal inflation -- that's all I'm saying.

I'll accept your claim, but it doesn't matter-- there are no theories of physics that have passed any observational tests whatsoever that include scalar potentials in GR. The whole idea of a scalar potential in GR is completely ad hoc, it seems like the simplest starting point but has passed no independent tests. It's very far from a physical theory that anyone should have any confidence in, so no one has any reason to claim it is more or less likely that inflation would be "eternal." Indeed, I doubt the idea would have any traction at all in the absence of anthropic thinking, and the perception of a "fine tuning problem."

I said this in response to your statement that you could apparently distinguish between "standard inflation" and "eternal inflation". As I've stated with the reasoning above, I don't believe that this is a useful operational distiniction.

I'm basing this on my perception of what is actually counted as mainstream astronomy, which I think is actually pretty unambiguous in this case. For example, an astronomy textbook can easily describe the inflation phenomenon and detail its predictive advantages, but they would all feel quite speculative, possibly even flaky, to go on about multiverses or eternal inflation. At some point, if you are in front of a classroom saying stuff, you want to feel that there is some observational basis to what you are telling people, you don't want to feel like a witch doctor (it's very discomfiting!).

Why is the model necessarily infinite? I would instead say that the model doesn't say one way or the other.

A model is an abstract mathematical structure, it has no idea what we are capable of observing. This model has two key features-- flatness, and the cosmological principle. Combined, it means it is formally an infinite model. If you want it to change somewhere beyond what we can observe, or cut out there, you'd have to add a third element to it, but what would be the point? What is beyond what we can observe will always be a simple mystery to us, as science must be fundamentally empirical or it is something else.

But, I want to point out that if we are ever able to pin down the form of the inflaton potential reliably, and, say, discover that it is a polynomial, with minimal assumptions (namely that the universe is larger than our Hubble patch) we are innevitably led to accept an eternal picture of inflation. Granted, we are not observing other pocket universes, but the consistency of the theory would in this case strongly imply their existence. This kind of indirect evidence has its place in the scientific method.

I accept your point that there might be theories that ultimately gain great popularity that suggest an interpretation in terms of eternal inflation, but the remainder of your point still sounds to me like the fallacy that language about science has fallen into over and over. No matter how much we may like our current model, its successes never demonstrate to us anything beyond what we have actually tested by experiment in similar domains of application, they only suggest new hypotheses and new tests. So no matter how much we like some simple model, it will never tell us that the universe actually undergoes eternal inflation, unless we have ample observational evidence that is not just an interpretation of a simple model. Didn't we make that mistake enough times?

I'm not saying we should never try to interpret our theories (like the "shut up and calculate" school, that nobody ever really adheres to), I would say that physics was invented as an arm of philosophy to try and inform philosophy about certain types of questions. But it has evolved from that launching point, and I'd say we should have learned by now that although good physics theories can inform our interpretations of reality, they tend to get overinterpreted when we are not careful in our language around what physics theories really are. Interpretations should be regarded as informative ways to think about the models, not descriptions of what is actually happening. Just look at the fuss in philosophical circles about Newton's laws and determinism and free will and divine providence and all that. If they had just recognized Newton's laws for what they are, a very nice model that makes no claims on how things actually work, they could have avoided most of the worst of it.

 

[twofish-quant]

I can't see how you can claim that without some physical basis for the cause of the inflation.

Since inflation occurs at energies associated with the nuclear force, you can reasonably assume that quantum field theory still works. You then can assume a mathematical form for the potential that triggers inflation, and then see what happens.

If you want to support that statement with some kind of physical theory, then you need to be able to say what observational tests that theory has satisfied, and there is a very long and exhaustive process that goes into gaining confidence in any such attempt.

In the case of inflation, it turns out that a lot of the predictions are independent of the details. This is good because it let's you compare with observations without knowing the details. This is also bad, because it means that you can't calculate things based on the observations.

How can you say that? The phenomenon is inflation, period. Saying it "should" happen eternally is not a phenomenological statement, it is a claim on some theory that has passed no tests other than what it was specifically built to pass (if that).

We aren't in the quantum gravity era in which we are doing total guess work. Inflation occurs at energies at which quantum field theory and general relativity are usable, and so you can make predictions based on QFT and GR. Where you don't know, you can put in an unknown variable.

There is a *lot* less mumbo-jumbo in inflation than one might think. It's important not to confuse inflation with quantum gravity.

For example, an astronomy textbook can easily describe the inflation phenomenon and detail its predictive advantages, but they would all feel quite speculative, possibly even flaky, to go on about multiverses or eternal inflation.

Multiverses are quite different from eternal inflation.

This model has two key features-- flatness, and the cosmological principle.

You are wrong. Flatness is not generally assumed in LCDM. (There is one situation where people will assume flatness, and that's when trying to figure out the equation of state of the cosmological constant from observations and that's because you can't tell if the results are due to EOS or to curvature.)

You are trying to teach cosmology (incorrectly) to people that have more experience in the topic than you do.

(I apologize if I'm getting harsh, but it's really frustrating trying to explain two simple points to someone that isn't listening, and I'm about to give up.)

The two simple points are:

1) the current model of cosmology does not **assume** flatness
2) inflation does not require undetectable curvature

If you accept those points then all of the philosophy becomes irrelevant, and whether those points are true or not are "textbook" issues that should be easy to resolve.

 

[Ken G]

That's false. Inflation occurs at grand unification energies, and while those are high they are still at the levels at which you can make testable predictions (i.e. proton decay).

We have a theory of grand unification. Had inflation occurred within what is describable that way, we'd already have a theory of inflation.

With inflation, we are at the edge of "known physics" but we aren't in the land of total speculation.

We are if we ask, will the inflation be eternal or not? If you think that is not true, give me one experiment that has been done or could be done with current technology that definitiverly comes out A if inflation is eternal, and not A if it isn't. The effort to use observations to distinguish models of inflation is at a very early stage, and is highly unproven to say the least. It's probably something a bit better than a complete flight of fancy, but there is still no detailed inflation theory that is anywhere close to mainstream consensus.

We have a ton of data in the form of CMB temperature fluctuations. Those were generated by inflation. The other thing is that inflationary theories produce lots of testable predictions, which is why it's hard to come up with one that works.

I have no issue with using theories to fit data, the issue is whether or not this will ever tell us if inflation is eternal or not! Of course it will not ever tell us that, theories don't tell us that unless we observe it to happen.

And I'm saying that you are wrong. Unknown does not mean unknowable.

What I said is unknowable is that is going on in domains that we cannot observe. That is indeed unknowable, although it is very easy to lie to ourselves that we can know this, and repeat the same mistake that has been repeated so many times in the history of physics we should certainly know better by now.

There are a set of possible observations that would indicate that the universe is finite and round. If we detect non-zero curvature and then if we pin down the amount of expansion from CMB, then we can show that the universe is finite and estimate it's diameter.

Which will again be a model, just like the current flat model is, and it will again not really tell us what is going on in the regions we cannot observe, just as the current model cannot. If we detect some miniscule curvature in the observable universe, why on Earth would we extrapolate that, as we would need to, to a volume hundreds or thousands of times larger than what we can observe? Is that kind of reasoning not exactly what led people to imagine the Earth was flat?

And that's a false statement. A small positive curvature is consistent with inflation and the current observational data.

Calculate the precision in the curvature you would need at the end of inflation to produce a flatness that was within, say, 0.1% of 1 today. Then come back and tell me this again with a straight face. That is the whole reason for the invention of anthropic thinking, to be able to have a straight face as we say that the numbers are unexpected by 100 orders of magnitude. Anyone who thinks that a theory like that is good, because they can embed it in 10¹⁰⁰ other universes and just pick the universe that works, has really lost track of what science is supposed to do-- explain our universe in terms of efects that we can actually observe! Embedding it in 10¹⁰⁰ other universes is no better than inventing chariots of fire in the heavens, which we also could not observe the properties of.

You keep making false statements about cosmology, such as the notion that inflation *requires* a non-zero curvature.

I think you mean zero curvature. And nothing you have said refutes that without invoking anthropic reasoning, which is dubious science that is certainly not mainstream outside of the subfields that favor it.

I've already given you papers in which cosmologists have presented models of inflation that are work with small positive non-zero curvature, which you haven't refuted.

You mean the papers that refer to eternal inflation? They just make my point-- they are based in anthropic thinking, which is required to get nonflat universes from inflation. That has been my entire point all along, the questionable nature of that argument. Sure you can get it published, but it is very far from mainstream astronomy, and I personally know few astronomers who would ever teach anthropic models of the universe to a class (expressly because they would feel like a witch doctor doing it).

Your understanding of inflation is simply incorrect. There's nothing in inflation or current cosmology that *requires* a flat, infinite universe.

Do you mean if you accept anthropic thinking? I've told you why I reject that as mainstream science, as does almost every astronomer I know (I know a lot, outside the subfield of speculative cosmology). What I want to know is this:
do you still hold to your claim in the absence of anthropic thinking, i.e., in a model where you just get one universe, not 10¹⁰⁰ to pick from to get the result you want?

Whether the universe if round or not is a purely observational issue.

Absolutely not, and this is the key point. Your statement would only have been true had we been able to observe the whole universe, which we already know we cannot do. You apparently think that if we observe a tiny curvature, it means the whole universe, beyond what we can observe, will match that same curvature. That is fallacious thinking, pure and simple, and has been wrong dozens of infamous times throughout the history of science.

One good thing about inflation is that it killed several anthropic arguments.

Inflation didn't do that, it is a theory. Theories don't kill theories, observations do.

Whether the universe if round or not is a purely observational issue.

Correction-- whether the observable universe is curved or flat is purely an observational issue! We already know what the whole universe is doing is not an observable issue, that's the point. What's more, the current evidence is that it is flat, a point that you seemed to dispute earlier. Whether or not it could be curved, and inflation still be a good model, seems to be a matter of whether or not one views anthropic thinking as valid scientific reasoning.

 

[twofish-quant]

We have a theory of grand unification.

We don't. We have several candidate theories, of which the simplest ones are known
false (proton decay). Also even in situations where we do have good theories for the underlying physics getting from that to observable predictions can be quite painful. No one has been able to calculate the proton mass for examplpe.

Had inflation occurred within what is describable that way, we'd already have a theory of inflation.We are if we ask, will the inflation be eternal or not?

We can't go from QCD -> mass of proton yet.

If you think that is not true, give me one experiment that has been done or could be done with current technology that definitiverly comes out A if inflation is eternal, and not A if it isn't.

The Guth paper points out that observation of curvature would rule out some models of eternal inflation.

What I said is unknowable is that is going on in domains that we cannot observe.

It's possible to make strong inferences about things that you can't directly observe. For example, we can't observe the core of the Earth directly, but that doesn't prevent us from saying meaningful things about it.

We already can make statements about parts of the universe outside of the observation radius.

Which will again be a model, just like the current flat model is, and it will again not really tell us what is going on in the regions we cannot observe, just as the current model cannot.

If you keep insisting that the current cosmological model requires that the universe be flat, then this conversation is going to go nowhere. I'm about to give up here.

If we detect some miniscule curvature in the observable universe, why on Earth would we extrapolate that, as we would need to, to a volume hundreds or thousands of times larger than what we can observe?

Because we can tell from observational data how much the universe inflated, and then this gives you the radius at which you can extrapolate local observations.

Also, a lot of scientific statements are of the form, if X then Y. If you argue that curvature can't be extrapolated, then you *must* believe that the universe is non-isotropic. You can then look for signs of non-isotropy.

Calculate the precision in the curvature you would need at the end of inflation to produce a flatness that was within, say, 0.1% of 1 today.

It's on the order of 10^-18. That's not zero.

The mass of the electron is 10^-31 kg. That's not also zero.

Also, the amount of curvature that you would need to produce a flatness that is within a factor of 100 of 1 is 10^-14. If you have any flatness that is within a factor of a million of 1, you are going to have something to explain.

That is the whole reason for the invention of anthropic thinking, to be able to have a straight face as we say that the numbers are unexpected by 100 orders of magnitude.

You are missing the point. The reason inflation is cool is that it *avoids* the need for anthropic thinking. Without inflation, you have to have this weird coincidence to have any sort of curvature that is within a factor of a million of what we observe. With inflation, you don't.

You mean the papers that refer to eternal inflation? They just make my point-- they are based in anthropic thinking, which is required to get nonflat universes from inflation.

No they don't. If you want, you can just say that the universe works that way. Also since the inflation mechanism is unknown, the statement that anthropic thinking is required to get non-flat universes is something without any basis.

Sure you can get it published, but it is very far from mainstream astronomy, and I personally know few astronomers who would ever teach anthropic models of the universe to a class

I know the cosmologist that published the paper that made anthropic models respectable. He has a Nobel prize in physics, and I presume he teaches the topic in his class in cosmology.

At this point, I don't think it's possible to have a decent class in cosmology without mentioning the anthropic principle. I'm personally skeptical of anthropic arguments, but it's an idea with enough backing that you can't avoid teaching it.

I've told you why I reject that as mainstream science, as does almost every astronomer I know (I know a lot, outside the subfield of speculative cosmology).

I don't *like* the anthropic principle, but it's certainly not "outside the bounds of mainstream science."

do you still hold to your claim in the absence of anthropic thinking, i.e., in a model where you just get one universe, not 10¹⁰⁰ to pick from to get the result you want?

Without inflation, you either have to chose fine-tuning or anthropic arguments to get any flatness < million. With inflation, you don't have to fine tune or use anthropic arguments to get that result. That's good.

Your statement would only have been true had we been able to observe the whole universe, which we already know we cannot do. You apparently think that if we observe a tiny curvature, it means the whole universe, beyond what we can observe, will match that same curvature.

No I don't. If we observe a tiny curvature, and the universe is isotropic and homogenity, then everything will match that curvature. We then look observational results which measure isotropy and homogenity to see what the limits on that are.

If it turns out that the universe is finite, then we could using observations to establish that the universe is isotropic within the radius of curvature of the universe.

Correction-- whether the observable universe is curved or flat is purely an observational issue! We already know what the whole universe is doing is not an observable issue, that's the point.

Not true. If the universe is finite then we can measure the entire universe. If it isn't then we can't. We don't know whether the universe is finite or not.

What's more, the current evidence is that it is flat, a point that you seemed to dispute earlier.

And I dispute it now. The current evidence is that the universe is within 0.01 of being flat. That's different from saying that it's flat. Also, there are some assumptions in the evidence that may not be true. The calculations assume GR is correct and that dark energy is the cosmological constant. If those are false, then the numbers could change.

As of 1995, the best numbers were that the universe had a curvature of -0.7. If it turns out that we aren't seeing dark energy, then we go back to those numbers.

Whether or not it could be curved, and inflation still be a good model, seems to be a matter of whether or not one views anthropic thinking as valid scientific reasoning.

You are changing your assertions. That's not necessarily a bad thing, but it will save me some effort if you now admit that non-zero curvature does not exclude inflation.

If you concede this point, then I don't see why raise anthropic principles. Guth only does so in his paper to reduce the search space of possible parameters.

Personally, I strongly dislike anthropic arguments. So let's reject the anthropic principle, and let's suppose we observe a positive curvature, I don't see the impact on inflation. There's enough evidence for inflation in the form of CMB background that I don't see what the issue is.

 

[Ken G]

Since inflation occurs at energies associated with the nuclear force, you can reasonably assume that quantum field theory still works. You then can assume a mathematical form for the potential that triggers inflation, and then see what happens.

So quantum field theory is now a theory of gravity? Does quantum field theory involve scalar gravitational potentials anywhere? We have laboratory evidence of such scalar potentials, which form part of the experimental basis of quantum field theory?

In the case of inflation, it turns out that a lot of the predictions are independent of the details.

Yes, that's what I meant by "standard inflation." But the key question all along here has been, should we count "eternal inflation", and the "multiverse", as "predictions that are independent of the details."? I certainly don't think so.

We aren't in the quantum gravity era in which we are doing total guess work. Inflation occurs at energies at which quantum field theory and general relativity are usable, and so you can make predictions based on QFT and GR. Where you don't know, you can put in an unknown variable.

But it's that "unknown variable" that is exactly the point. We do throw in a cosmological constant into GR, but only because there is an inescapable experimental need for it, and it causes a great deal of controversy. Models of inflation are nowhere near the kind of observational support of LCDM, and even given that, the recent Nobel prizes are viewed by many to be rather premature. I've never seen anything like a mainstream consensus about the proper details of a working inflation theory, but perhaps now the distinctions we are drawing are becoming somewhat subjective.

There is a *lot* less mumbo-jumbo in inflation than one might think. It's important not to confuse inflation with quantum gravity.

All right, I can grant that point, but it's not clear if that is saying something all that great about inflation models-- or something bad about loop quantum gravity!

Multiverses are quite different from eternal inflation.

Not in regard to the salient issue in this thread, which is, do we think that inflation leads to unmeasurable curvature without invoking some kind of multiverse/eternal inflation to allow us to view our theory as generic rather than incredibly finely tuned. I agree that if one does like to think anthropically, one can view inflation as a credible way to get some tiny but measurable curvature, but if one rejects that thinking as a way to validate a theory, then the detection of curvature would require looking for other theories than inflation.

You are wrong. Flatness is not generally assumed in LCDM. (There is one situation where people will assume flatness, and that's when trying to figure out the equation of state of the cosmological constant from observations and that's because you can't tell if the results are due to EOS or to curvature.)

I know it is not assumed in LCDM, that's the point-- it is a conclusion of LCDM. To wit, it is a conclusion that we successfully model the history of the universe by adopting a flat model, and furthermore, we have no reason to adopt any other model (by Occam's razor), and finally, if inflation is to be viewed as a good model (and anthropic arguments viewed as unscientific), then this will always be true. That doesn't mean we can't detect curvature, it means that if we do, we are going to start looking for alternatives to inflation the very next day, because embracing questionable anthropic arguments is going to feel like a real band-aid for inflation.

You are trying to teach cosmology (incorrectly) to people that have more experience in the topic than you do.

I'm not teaching cosmology, I'm pointing out the difference between a model, and a claim on the truth about the universe. Look at the title of the thread-- "the shape of spacetime" is a description of a mathematical model. That model exists, it is called LCDM. It is a flat model, because it is consistent with flatness, and models are always as simple as they can be yet still fit the data. It is not a claim on what we cannot observe, and never will observe. These are all just facts.

The two simple points are:

1) the current model of cosmology does not **assume** flatness

I never said it did. This is a result of model-making-- we use a flat model because we can, that's what makes it our best model. My entire point is that this does not make claims about the universe beyond what we can see, and what's more, we already know we cannot make claims about that, expressly because we know we will not be able to see it. We can weave a nice tale using eternal inflation and anthropic thinking, but every culture in history has weaved a nice creation myth-- that sure doesn't make it science. Empirical tests, not satisfying stories, is what makes something science.

2) inflation does not require undetectable curvature

Detectable curvature makes inflation a far weaker theory, it forces you to invoke anthropic thinking. I think that would motivate alternatives almost immediately, should curvature ever be detected, which seems unlikely. People also look for net rotation of the universe, there's no harm in looking.

 

[twofish-quant]

So quantum field theory is now a theory of gravity? Does quantum field theory involve scalar gravitational potentials anywhere? We have laboratory evidence of such scalar potentials, which form part of the experimental basis of quantum field theory?

In the inflationary era, the energies are low enough so that you can handle QFT and GR separately. In that situation, any scalar potentials from QFT just act as classical potentials. Also any spin-0 particle can be represented as a scalar field. You can do QFT with spin-0 nuclei and the math works out.

Also we do have cosmological evidence of a scalar potential. Dark energy.

Yes, that's what I meant by "standard inflation." But the key question all along here has been, should we count "eternal inflation", and the "multiverse", as "predictions that are independent of the details."?

You keep changing the key question. "Multiverses" don't have much to do with inflation. "Eternal inflation" is merely one scenario among half a dozen other inflationary scenarios, and I don't quite see it the point of focusing on that particularly one.

But it's that "unknown variable" that is exactly the point. We do throw in a cosmological constant into GR, but only because there is an inescapable experimental need for it, and it causes a great deal of controversy.

And we throw in curvature for the same reason.

[QUOTE Models of inflation are nowhere near the kind of observational support of LCDM, and even given that, the recent Nobel prizes are viewed by many to be rather premature. I've never seen anything like a mainstream consensus about the proper details of a working inflation theory[/QUOTE]

This is false. There are some very strong constraints on what you need in an inflationary theory.

Not in regard to the salient issue in this thread, which is, do we think that inflation leads to unmeasurable curvature without invoking some kind of multiverse/eternal inflation to allow us to view our theory as generic rather than incredibly finely tuned.

I don't see why this is a relevant question. The problem is that if you have any flatness coefficient that's less than a million, you are going to run into the same problem, and it doesn't matter whether its 0, 0.01, or 1000.

I know it is not assumed in LCDM, that's the point-- it is a conclusion of LCDM. To wit, it is a conclusion that we successfully model the history of the universe by adopting a flat model, and furthermore, we have no reason to adopt any other model (by Occam's razor)

This is false.

1) The data says that the universe is within 1% of flat. That's not flat.

2) Assuming flatness doesn't simplify the model. Even if the *average* curvature of the universe is zero, LCDM calculates the "variation" of curvature. So you are going to have to include spatial curvature no matter what you do.

3) LCDM contains some assumptions which are not completely firm. In particular it makes assumptions about dark energy, and if those are false, then we go back to curvature = -0.7.

4) You are entitled to your personal opinions, but the views that you are putting forth are not scientific consensus

Finally, if inflation is to be viewed as a good model (and anthropic arguments viewed as unscientific), then this will always be true.

You keep asserting this and it's false. Aside from the solving the flatness and horizon problems, inflation gives us a good mechanism to seed the initial density perturbations that are needed to model CMB.

That doesn't mean we can't detect curvature, it means that if we do, we are going to start looking for alternatives to inflation the very next day, because embracing questionable anthropic arguments is going to feel like a real band-aid for inflation.

This is false, and it's provably false.

Before the discovery of dark energy in 1998, the curvature of the universe was believed to be -0.7, but inflation was taught as part of standard cosmology. If we do find curvature, it's going to impact which inflation models are viable, but it's not going to kill the inflation mechanism.

Look at the title of the thread-- "the shape of spacetime" is a description of a mathematical model.

No its not. It's an observational reality.

That model exists, it is called LCDM. It is a flat model, because it is consistent with flatness, and models are always as simple as they can be yet still fit the data.

We are going in circles.

Here is LCDM

http://map.gsfc.nasa.gov/resources/camb_tool/index.html

You can change the knobs to get all sorts of curvatures.

My entire point is that this does not make claims about the universe beyond what we can see, and what's more, we already know we cannot make claims about that, expressly because we know we will not be able to see it.

Yes it does make claims. Those claims may be incorrect, but making incorrect claims is a good thing. LCDM does indeed make claims about the unobservable universe. Those may be incorrect, but that's an observational issue.

Detectable curvature makes inflation a far weaker theory, it forces you to invoke anthropic thinking.

No it doesn't. Also inflation reduces the need for anthropic thinking. Within inflation you don't have to fine tuning your initial conditions as much.

Also you can also get away from anthropic thinking by invoking fine tuning.

People also look for net rotation of the universe, there's no harm in looking.

Sure...

http://arxiv.org/abs/astro-ph/0008106

 

[Ken G]

We don't. We have several candidate theories, of which the simplest ones are known

But then you are saying that inflation does not represent unknown physics, because it's just QFT and GR at the grand unification scale, but that also we don't have a theory at the grand unification scale! You are contradicting your own argument.

The Guth paper points out that observation of curvature would rule out some models of eternal inflation.

Yes, and note that just means that even with anthropic thinking inflation models do not necessarily survive the detection of curvature. That only strengthens what I'm saying, if you have to invoke eternal inflation and it still doesn't necessarily help.

We already can make statements about parts of the universe outside of the observation radius.

I am definining the "observable universe" to be whatever we have direct observational constraints on. When we look for curvature, what we see has some kind of physical radius associated with it, that includes the full sequence of inferences involved. We already know that will never be large enough to describe a closed universe, which is my point.

If you keep insisting that the current cosmological model requires that the universe be flat, then this conversation is going to go nowhere.

Where on Earth did you get the idea this conversation has had anything whatever to do with that claim? Have you been reading my words? I don't think that at all, and indeed argued strenuously against that the entire time. I think your frustration is coming from not listening.

If you argue that curvature can't be extrapolated, then you *must* believe that the universe is non-isotropic. You can then look for signs of non-isotropy.

You are missing the actual alternative there-- you just can't tell if it is isotropic or not, if all you detect is some teeny average curvature, and you simply accept that you won't get to tell, because you won't. You certainly don't have to believe it is non-isotropic, that is simply incorrect logic.

It's on the order of 10^-18. That's not zero.

Thank you for the number, that's helpful. Yes I know it's not zero, obviously, that's why I asked for it. The point is, you would find yourself in a position that you are advocating a theory that includes a parameter that must be specified to that degree of precision, based on observations with a precision that is probably 14 orders of magnitude less than that, and even GR itself is not established to that level of precision. That is a horrendous state of affairs, for a predictive theory to claim, there really would be nothing left of inflation if it had to be that precise of a theory to mean anything. It's what requires anthropic thinking to even suggest it with a straight face.

Also, the amount of curvature that you would need to produce a flatness that is within a factor of 100 of 1 is 10^-14. If you have any flatness that is within a factor of a million of 1, you are going to have something to explain.

Hence inflation, yes. Inflation is our explanation of flatness, and as such, it makes for a lousy explanation for very-near-but-measurably-not-flatness. A lousy explanation, that is, without anthropic thinking.

You are missing the point. The reason inflation is cool is that it *avoids* the need for anthropic thinking.

Only if the universe is not measurably curved, that is the whole point. That's also what Guth is saying-- as soon as you allow a detection of curvature, you are immediately thrust into an eternal inflation scenario, which is anthropic thinking-- we get to select the special inflation event that allowed us to be here, out of a vast number that have to actually occur.

Without inflation, you have to have this weird coincidence to have any sort of curvature that is within a factor of a million of what we observe. With inflation, you don't.

Obviously, that is quite central to my entire point. But the price you pay is that you succeed too well, if you ever detect any curvature. Immediately you are up to your neck in the anthropic escape hatch.

No they don't. If you want, you can just say that the universe works that way.

No, because that is the kind of statement you make about a measurement, not about a theory. You have to justify a theory, you don't get to say "the universe works that way", unless you are a witch doctor. You don't have to justify an observation, for that you can say "that's just how it is". How it works is an entirely different kettle of fish, that has to have some simplfying quality.

I know the cosmologist that published the paper that made anthropic models respectable. He has a Nobel prize in physics, and I presume he teaches the topic in his class in cosmology.

Not terribly surprising, is it, that a multiverse enthusiast would find multiverse arguments convincing? Do you think it's hard to find examples of highly decorated physicists who have non-mainstream ideas about cosmology that they might teach in their classes? What do you think Hannes Alfven taught, or Geoffrey Burbidge, or Hoyle? Speculation is fine in science, but calling it sound physics is another matter. What is viewed as "respectable" is largely political, it is what is viewed as mainstream that matters most.

At this point, I don't think it's possible to have a decent class in cosmology without mentioning the anthropic principle. I'm personally skeptical of anthropic arguments, but it's an idea with enough backing that you can't avoid teaching it.

You can "teach the controversy", if you like, but any self-respecting scientist who does that is going to be very clear that they have left the building of mainstream or empirically supported science. They are going to start feeling like a witch doctor if they say "here is what astronomers have accepted as the truth of our universe."

I don't *like* the anthropic principle, but it's certainly not "outside the bounds of mainstream science."

Yes it is, the way we use the term here (the strong version). The weak version is just a statement of fact, but the idea that our universe is selected out of many and this allows us to feel happy about highly fine-tuned theories is nothing short of a cop out. Science is about explaining what we observe by testing our hypotheses, not feeling good about what we observe by invoking things we cannot, or claiming that parameters that have values that we already know they must have is somehow a prediction of anthropic thinking. I don't think working astronomers are at all happy about anthropic thinking, it's largely a playground of people who go to meeting with other anthropic-thinkers. It is a very long way from catching on in the mainstream.

Without inflation, you either have to chose fine-tuning or anthropic arguments to get any flatness < million. With inflation, you don't have to fine tune or use anthropic arguments to get that result. That's good.

Except once again your statement only works if no curvature is detected, and is in exact agreement with everything I've said about inflation and curvature.

You are changing your assertions.

Not actually, because I have always rejected anthropic thinking as an allowable justification for a scientific theory. When you do that, all my previous statements are perfectly consistent with what I'm saying now. I'm just clarifying this better now.

That's not necessarily a bad thing, but it will save me some effort if you now admit that non-zero curvature does not exclude inflation.

It has always been obvious in this discussion that any inflation theory could precisely choose its parameters to get any curvature today. That's the meaning of a monotonic function, is this not completely obvious? The actual context of the discussion is how one of the main reasons for the inflation model, to remove the absurd fine-tuning of the curvature in the initial conditions, would be lost if inflation had to produce a similarly absurd fine tuning (I believe you quoted the number 10^-18) if the post-inflation curvature had to increase to a tiny level we could observe today but haven't yet, like the 10^-4 number quoted in that Guth article. That's exactly why anthropic thinking, in the form of eternal inflation, would need to return in that eventuality, which is my whole point.

Personally, I strongly dislike anthropic arguments. So let's reject the anthropic principle, and let's suppose we observe a positive curvature, I don't see the impact on inflation. There's enough evidence for inflation in the form of CMB background that I don't see what the issue is.

Well I'm glad we can agree to reject anthropic thinking, but if we observe positive curvature, calculate the post-inflation curvature that would be needed to explain that. How is that so different from the very anthropic thinking that would be needed to explain a universe with no inflation at all?

 

[Caramon]

Just as an outsider reading this whole twofish-Ken G debate going on, I'll have two comments to make:

1) It has been very entertaining and as an undergraduate I have learned a lot from looking up a paper on a topic I did not know about when it was mentioned.

2) Twofish looks like he has a better understanding of all of the topics, and I think I found a contradiction or two in Ken G's arguments.

Keep going! I'm learning a lot. :D

 

[twofish-quant]

But then you are saying that inflation does not represent unknown physics, because it's just QFT and GR at the grand unification scale, but that also we don't have a theory at the grand unification scale!

There are different levels of "known-ness." Our best guess right now is that GUT physics is such that both QFT and GR are valid, and there is no need to invoke weird quantum gravity. The form of the Langrangian at GUT energies is unknown, but you can put in different equations and see what happens.

When we look for curvature, what we see has some kind of physical radius associated with it, that includes the full sequence of inferences involved. We already know that will never be large enough to describe a closed universe

We don't know this. It's perfectly possible that we will observe a small but finite radius of curvature and use CMB spectrum to establish isotropy within the radius of curvature.

You just can't tell if it is isotropic or not, if all you detect is some teeny average curvature, and you simply accept that you won't get to tell, because you won't.

You can look for anisotropy within CMB and use that to constrain the radius in which we expect the universe to be isotropic.

The point is, you would find yourself in a position that you are advocating a theory that includes a parameter that must be specified to that degree of precision, based on observations with a precision that is probably 14 orders of magnitude less than that, and even GR itself is not established to that level of precision.

Which means that you can't use nucleosynthesis calculations to constrain flatness, but you can use local observations to do it. What happens is that whatever the value of flatness is at the end of inflation, it gets multipled by 16 orders of magnitude to the point that it may well be detectable if you use late universe observations.

Obviously, that is quite central to my entire point. But the price you pay is that you succeed too well, if you ever detect any curvature. Immediately you are up to your neck in the anthropic escape hatch.

No you aren't. If you detect curvature, then you look for the energy scale at which the inflation ends. At if it matches any sort of physical constant, then you have nothing to explain. The reason that inflation gets rid of anthropic and fine tuning is that anything that needs to get explained gets put into the somewhat unknown but not unknownable physics of inflation.

The actual context of the discussion is how one of the main reasons for the inflation model, to remove the absurd fine-tuning of the curvature in the initial conditions, would be lost if inflation had to produce a similarly absurd fine tuning (I believe you quoted the number 10^-18) if the post-inflation curvature had to increase to a tiny level we could observe today but haven't yet, like the 10^-4 number quoted in that Guth article. That's exactly why anthropic thinking, in the form of eternal inflation, would need to return in that eventuality, which is my whole point.

And that point is wrong.

The point of inflation is that you now have the ability to create a way of producing small but not zero curvatures *naturally*. For example, under some models of inflation, the universe expands until the curvature is small enough to allow quantum mechanical tunneling. What would happen in this situation is that the universe would expand until the curvature gets very small, particles tunnel out, and inflation ends, giving you a tiny curvature that blows up to a small one.

http://ned.ipac.caltech.edu/level5/Albrecht/Alb3_3.html

That might not work, but the point is that the thing about inflation is that it provides an alternative to anthropic and fine-tuning arguments. We'll only have to go back to anthropic and fine-tuning arguments once we run out of scenarios for inflation.

Well I'm glad we can agree to reject anthropic thinking

I didn't say that I reject. I said I don't like it. I'll accept it only when there are no alternatives. The point of inflation is that it gives you alternatives.

but if we observe positive curvature, calculate the post-inflation curvature that would be needed to explain that.

And if it turns out to be comparable to some subatomic scale, we have nothing to explain.

How is that so different from the very anthropic thinking that would be needed to explain a universe with no inflation at all?

Because you have unknown but not unknowable physics that you can look at before giving up.

It's pretty simple. If I flip a coin 50 times, and it all comes up heads, then I don't assume that God did this. I don't assume that there are a billion other coin flippers. My first assumption is that the coin is somehow rigged to always come up heads.

It's only after that I convince myself that the coin isn't rigged that I end up with headaches.

The thing about inflation is that it provides enough unknown physics so that you can argue that somewhere in there, the coin is rigged. If it turns out that the universe ends inflation with whatever curvature, then we look at the details of inflation to come up with reasons why the coin was rigged to come up with that value. It's only after eliminating the possibility that the coin is rigged that you end up with a philosophical problem.

If you go (initial conditions)->(inflation)->(current universe), then you end up with a black box in which you can try to invent some physics that explains the current set of parameters. If you go (initial conditions)->(current universe), then you don't have a place to hide a rigged coin.

If you argue initial conditions, you are basically saying "God did it." Instead of saying "God did it" you can say "inflation did it" which is different because inflation is subject to scientific inquiry.

 

[Ken G]

2) Twofish looks like he has a better understanding of all of the topics, and I think I found a contradiction or two in Ken G's arguments.

You are more than welcome to state what you see as a contradiction, and then I can tell you if you have interpreted me correctly. Let me caution you against accepting twofish-quant's versions of what I'm saying, they are often not even close.

 

[Ken G]

We don't know this. It's perfectly possible that we will observe a small but finite radius of curvature and use CMB spectrum to establish isotropy within the radius of curvature.

Where did I ever say we couldn't?? Again you are putting words in my mouth and changing my argument. Of course we could observe that, we could observe anything that doesn't contradict what we've already seen. But so what? Are you going to claim that if we observe a piece of the universe that has a consistent and tiny curvature, that this implies something about the rest of the universe that we do not observe? By what form of logic would you ever be able to do that? If we can barely observe the small curvature, just how precisely do you think we can establish its consistency, and how accurately could we ever extrapolate that with confidence? No, you are confusing the model we would create to fit that data with an assertion about something that we simply would not know and would not have any good reason to think that we know. You are confusing what goes into a good model (which includes Occam's razor) with what goes into knowledge about the universe (which does not).

You can look for anisotropy within CMB and use that to constrain the radius in which we expect the universe to be isotropic.

No we certainly could not form any such scientifically justified expectation, any more than a person standing in a volcanic crater can expect the whole Earth to be concave. The cosmological principle is a simplifying principle used in good models, it is not a constraint on something we've never seen and never will see. Not if you are doing science instead of generating plausible belief systems.

No you aren't. If you detect curvature, then you look for the energy scale at which the inflation ends. At if it matches any sort of physical constant, then you have nothing to explain.

Sure you do, if you detect curvature today. You would then have to explain why the physical constant had just the value necessary to let inflation end at a time that would lead to some small but measurable curvature today! That's my point, such a detection would strip the inflation model of most of its primary purpose, which is to make our universe seem natural or plausible-- without anthropic reasoning.

http://ned.ipac.caltech.edu/level5/Albrecht/Alb3_3.html

Thank you for this interesting article, but I hardly see where it is backing your claims, indeed I see several points that are completely in concert with my current understanding, including:

"The upshot is that additional scalar fields abound, at least in the imaginations of particle theorists, and if anything the problem for cosmologists has been that there are too many different models. It is difficult to put forward anyone of them as the most compelling. This situation has caused the world of cosmology to regard the ``inflaton'' in a phenomenological way, simply investigating the behaviors of different inflaton potentials, and leaving the question of foundations to a time when the particle physics situation becomes clearer. "

I interpret that as saying that inflation models are somewhat "swinging in the dark", lacking sufficient constraints from established physics to be able to judge their plausibility, just as I thought.

And:
" Fine tuning of potential parameters is generally required to produce sufficient inflation in slow roll models. Essentially all current models of inflation use the slow roll mechanism."

Which I interpret as flying completely in the face of your argument that the point of inflation is to remove the need for fine tuning! Admittedly the fine tuning is not as horrendous as it would be without inflation, which is its raison d'etre, but the article has said nothing about ending up with a measurably curved universe today, and that would exacerbate the fine tuning problem drastically.

And if it turns out to be comparable to some subatomic scale, we have nothing to explain.

Being comparable won't cut it, it has to be exactly the atomic scale. In fact, if it came out close, you would know the atomic scale much more precisely from the inflationary constraints than anything we could actually measure. But if we observe finite curvature, now you have to explain why that atomic scale is so finely tuned as to produce that. That's why finite curvature today would be bad news for inflation proponents, the plausiblity of their exercise would drastically diminish.

Because you have unknown but not unknowable physics that you can look at before giving up.

But you are just hoping, you can also buy a lottery ticket if you want to get rich. Yes, it may be the only means you have for getting rich, but that doesn't make it a good strategy for making a living.

If I flip a coin 50 times, and it all comes up heads, then I don't assume that God did this. I don't assume that there are a billion other coin flippers. My first assumption is that the coin is somehow rigged to always come up heads.

That's not a very good analogy though. A better one would be to generate sequences of numbers, have them all come out the same, and hope that this won't seem finely tuned if what they come out to is the decimal expansion of pi! And even if it did come out that way, you still couldn't explain why a parameter equal to the decimal expansion of pi would be precisely in the range of parameters that would end up with tiny but measurable curvature, that would still be a complete mystery, and a finely tuned one at that.

The thing about inflation is that it provides enough unknown physics so that you can argue that somewhere in there, the coin is rigged.

Exactly, you can get it to do whatever you like. Just like the article said, there are way too many possibilities. The problem is, they would all be finely tuned, and extremely so if you need the model to end up with finite measurable curvature today.

If you go (initial conditions)->(inflation)->(current universe), then you end up with a black box in which you can try to invent some physics that explains the current set of parameters. If you go (initial conditions)->(current universe), then you don't have a place to hide a rigged coin.

Sure you do, you put it in the physics of the initial conditions, like a brane collision or some such thing. The point is, whatever model you come up with is going to have some parameters in it, and even if those parameters come from some existing physics, it's still fine tuned if you need to get a finite measurable curvature today.

 

[twofish-quant]

Are you going to claim that if we observe a piece of the universe that has a consistent and tiny curvature, that this implies something about the rest of the universe that we do not observe?

Yes. I claim this. If we observe a piece of the universe that has a consistent curvature then we can conclude that either the parts of the universe that we can't directly observe are different *or* that the universe as a whole has a certain shape.

No, you are confusing the model we would create to fit that data with an assertion about something that we simply would not know and would not have any good reason to think that we know.

We can narrow down the alternatives.

Sure you do, if you detect curvature today. You would then have to explain why the physical constant had just the value necessary to let inflation end at a time that would lead to some small but measurable curvature today!

Why? I would have no need to do that anymore than I need to explain why the mass of the electron is such that I get a nice cup of coffee, or why the boiling point of water happens to be what it is.

If I flip a coin 50 times in a row and I find it's all heads, I have something to explain. If I find that it happens to be a two headed coin, then there is nothing to explain. The universe is set up so that no matter what the initial conditions are, it ends up a certain way and there is no fine tuning or anthropic argument necessary.

I interpret that as saying that inflation models are somewhat "swinging in the dark", lacking sufficient constraints from established physics to be able to judge their plausibility, just as I thought.

Exactly,

Which is why:

1) we need more high precision cosmological and particle physics experiments

2) it's not the end of the world if we find out that the universe has a curvature. If that happens we take our hundred or so inflation models and cross out the one's that require zero curvature. If it happens that we don't find curvature, we take a red pen and cross out the ones that require non-zero curvature.

Which I interpret as flying completely in the face of your argument that the point of inflation is to remove the need for fine tuning!

Slow roll models require fine tuning. That's why people don't like slow roll models.

Being comparable won't cut it, it has to be exactly the atomic scale. In fact, if it came out close, you would know the atomic scale much more precisely from the inflationary constraints than anything we could actually measure.

Cool isn't it.

But if we observe finite curvature, now you have to explain why that atomic scale is so finely tuned as to produce that.

No you don't. If the magic number is 10^-32, then after X years, I'll see curvature of 0.01. If the magic number is 10^-50, then after X+epsilon years, I'll see a curvature of 0.01. Seeing a finite curvature is independent of the magic minimum number. If the universe has curvature, then what will happen is that it will eventually take every value between 0 and infinity, or 0 and -1 (assuming no cosmological constant at which point curvature will reach a maximum).

So the reason the universe has the curvature that it has is we happen to be around in the time that it happens to have a the current value. If it is 0.01 today, it will be 0.02 in X billion years 0.3 after some more time, and eventually it's going to plop to some large value at which point dark energy takes over.

But you are just hoping, you can also buy a lottery ticket if you want to get rich.

No. I happen to dislike anthropic arguments, and I suggest that we first get rid of all of the non-anthropic possibilities before we even start to consider anthropic ones. As long as there are any plausible non-anthropic mechanisms to eliminate, I suggest we get rid of those before going anthropic.

And even if it did come out that way, you still couldn't explain why a parameter equal to the decimal expansion of pi would be precisely in the range of parameters that would end up with tiny but measurable curvature, that would still be a complete mystery.

If I take a pack of playing cards and deal them, and I have them all in order. That would be weird. However, if I just deal them and I get some random sequence, that wouldn't be. So I find out when inflation ends, and it's some random number. So what?

Sure you do, you put it in the physics of the initial conditions, like a brane collision or some such thing. The point is, whatever model you come up with is going to have some parameters in it, and even if those parameters come from some existing physics, it's still fine tuned if you need to get a finite measurable curvature today.

No it's not. If I have inflation and the cosmological constant isn't high, then at some point in the life of the universe someone *will* see a curvature of 0.001. Once you invoke inflation then most observers at within a finite universe will see a measurable curvature. Once I invoke inflation, I can change when "today" is. If the minimum curvature value was 10^-16, then "today" is X years post inflation. If it's 10^-13, then "today" is X - epsilion years. If it's 10^-30, then "today" is X + epsilon years.

As far as why I see a curvature of 0.001 rather than 0.002, that's like asking why I was born in the late-1960's rather than in the 1980's, there's nothing to explain. Once you have *any* positive curvature in the universe and you have low enough dark energy, then *someone* is going to see a curvature of 0.001, and it might as well be you.

 

[bapowell]

I can't see how you can claim that without some physical basis for the cause of the inflation. If you simply assert that inflation occurred early in our universe, that is a statement that has nothing to do with eternal inflation. If you want to support that statement with some kind of physical theory, then you need to be able to say what observational tests that theory has satisfied, and there is a very long and exhaustive process that goes into gaining confidence in any such attempt. That currently just does not exist, so for the mainstream, inflation is just a statement of a phenomenon, not a theory, and no claims can be made on how likely or often it "should" occur.

A couple points I'd like to make in response to this. You make the statement here, and elsewhere throughout this thread (and I'm paraphrasing) that inflation has no physical basis, is not a theory and just a phenomenon, is flaky, has not passed experimental muster, etc. I disagree with this stance. Firstly, I don't know what precisely you mean by phenomenon, but I suppose you mean that it is an idea or statement about the early universe -- that it underwent exponential expansion early on -- but that there is a lack of understanding for how this could happen and no observational evidence that currently helps shape an underlying theory. I would argue that both of these assertions lack merit.

First, there is a mechanism by which inflation can be achieved within GR, and so we already have more than a mere phenomenon. This mechanism does make use of hypothetical scalar fields, which you claim is ad hoc. (So, I must ask, are you equally skeptical of gauge theories and spontaneous symmetry breaking?) Keep in mind that the stress-energy that drives inflation need not be a fundamental scalar, it only needs to have an effective equation of state that satisfies w &lt; -1/3. Yes, we don't know precisely what the source of this stress-energy is, but that does not demote inflation to a mere ad hoc phenomenon.

Second, I would argue that there is a wealth of data supporting an early inflationary epoch. You claimed earlier than inflation makes not testable predictions beyond that which it was constructed to explain. I'm not sure I agree; first, what would you say inflation was constructed to explain? Flatness? Lack of monopoles? Resolve the horizon problem? I suppose that question can only be answered by learning the intent of the scientists who built the theory. I would say that even if we claim these were the prescribed goals of the theory, the discovery that inflation could generate the seeds of large scale structure was certainly not apparent at its conception. This realization came later, and it constitutes a definitive prediction of the inflationary proposal. So, we have a hypothesis: that a period of exponential expansion took place in the early universe, driven by a source of stress-energy with the quantum numbers of the vacuum. There are observations that address the first part of the hypothesis -- the exponential expansion. These are flatness of the observable universe, smoothness of the CMB together with its anisotropy, lack of monopoles, the presence of superhorizon-scale correlations in the temperature and polarization anisotropies in the CMB, and some others. But there are also observations that address that latter part of the hypothesis -- that a source with the quantum numbers of the vacuum drove the expansion. Such a source can be effectively modeled as a scalar field. We know certain facts about this field: it must have a potential energy that both supports inflation and ends it. We know it must have a shape that supports a sufficient amount of inflation. In its simplest form consistent with these requirements, it also makes predictions: namely, that the density perturbations will be adiabatic, Gaussian, and nearly scale invariant.

Now, taking the above into consideration, I have a predictive framework that does indeed rely on one major assumption -- the existence of an effective field with the quantum numbers of the vacuum. We have good reason to suspect that such fields exist, if our studies of symmetry breaking and gauge theories have anything to say about it. And within the above framework, I can begin to constrain my scalar potential; without understanding how inflation arises from the SM or some extension of it, this is a purely phenomenological endeavor since it is solely driven by data. This is what I mean by phenomenological. And from this approach, I can discover, by observations of the observable universe alone, whether the potential that drove inflation in our Hubble patch is operative elsewhere in the universe. It doesn't matter that I don't know how exactly the inflaton arises from supergravity or some other theory. The data, together a suitable application of Occam's razor, are sufficient.

And I must caveat this discussion by saying that I am not a proponent of eternal inflation or of multiverse theories per se; I have no vested interest in their veracity. But I think it is too constrictive to maintain your tact that unless it is strictly observed that it has no place in science. Many things that belong in mainstream science have not been strictly observed but only inferred or implied by the strict consistency of theories that have been supported by other observations.