Is the universe finite or infinite?

[Arifz]

Does the universe has boundaries?, is it finite?

 

[mathman]

Universe does not have a boundary. Finite or infinite is an open question.

 

[Arifz]

Universe does not have a boundary. Finite or infinite is an open question.

But there is no such thing as infinity in physics !

 

[haruspex]

But there is no such thing as infinity in physics !

Probably, but it's hard to be sure. Certainly the visible universe is finite and bounded. According to the inflationary theory of the big bang, space expanded faster than the speed of light for a while, so there are regions from which the light will never reach us.

But more interesting is what mathman said about the finite case. The universe can be finite in volume yet have no boundary. It depends on the topology. Imagine space as a cube, but in which each point of the left side is the same place as the point straight across from it on the right side. Similarly top/bottom and back/front. If you wander off through one face you just reappear out of the opposite face. And you wouldn't notice anything special, because where you choose the faces to be is arbitrary. Every point is as good as any other. (Topologically this would be a 3D torus, I think.)

 

[phinds]

But there is no such thing as infinity in physics !

Oh? Can you prove that? Do you have an accredited references to back up such a categorical statement?

 

[jackmell]

I believe there is a simple solution to this problem and it is based on behavior all through the Universe so I do not believe it is an inappropriate stretch to apply it to the entire Universe: we observe phenomena in the Universe having critical points in their dynamics. Breaching such a point often causes the dynamics of the phenomenon to change qualitatively and by doing so, the rules change. For example asking what does swimming mean beyond the critical point of freezing? What happens to a hydrogen atom beyond the critical point of fussion? In a small section of the ground it looks flat, even my whole yard. But it's not always flat, beyond the horizon the rules change and asking whether the Earth is infinitely flat or we just fall off is simply not following the new rules of a spherical Earth in a gravity field.

Therefore, in regards to a "size" of the universe, I do not think it is unreasonable to suggest at some large "size", a critical point is reached, the rules change, the concept "volume" loses meaning, and asking for a "size" of the Universe beyond that point is simply not following the new rules.

 

[Arifz]

Oh? Can you prove that? Do you have an accredited references to back up such a categorical statement?

I think the big bang "Theory" can proves it, however I still don't know what do we mean by "universe", is it the space that we know, or it also inclues beyond space "Vacume !". What do you call the "No Space/No Time" before the big bang?!

 

[Arifz]

I believe there is a simple solution to this problem and it is based on behavior all through the Universe so I do not believe it is an inappropriate stretch to apply it to the entire Universe: we observe phenomena in the Universe having critical points in their dynamics. Breaching such a point often causes the dynamics of the phenomenon to change qualitatively and by doing so, the rules change. For example asking what does swimming mean beyond the critical point of freezing? What happens to a hydrogen atom beyond the critical point of fussion? In a small section of the ground it looks flat, even my whole yard. But it's not always flat, beyond the horizon the rules change and asking whether the Earth is infinitely flat or we just fall off is simply not following the new rules of a spherical Earth in a gravity field.

Therefore, in regards to a "size" of the universe, I do not think it is unreasonable to suggest at some large "size", a critical point is reached, the rules change, the concept "volume" loses meaning, and asking for a "size" of the Universe beyond that point is simply not following the new rules.

Very logical explanation...Thanks.

 

[Astronuc]

"Space," it says, "is big. Really big. You just won't believe how vastly, hugely, mindbogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space, listen..." - Douglas Noel Adams, Chapter 8, The Hitchhiker's Guide to the Galaxy, Earth Edition, 1979


Paraphrased - "The Universe is Big. Really big. It may seem like a long way to the corner chemist, but compared to the Universe, that's peanuts."
http://astro.gmu.edu/classes/a10695/notes/l01/l01.html


The Hitchhiker's Guide to the Galaxy offers this definition of the word "infinite".

Infinite: Bigger than the biggest thing ever and then some. Much bigger than that in fact, really amazingly immense, a totally stunning size, real "wow, that's big," time. Infinity is just so big that, by comparison, bigness itself looks really titchy. Gigantic multiplied by colossal multiplied by staggeringly huge is the sort of concept we're trying to get across here.
http://www.acc.umu.se/~ola/hitchhik.htm


The challenge for one is not to let the vastness of the universe boggle one's mind.

 

[phinds]

I think the big bang "Theory" can proves it

I did not ask what you think, I asked what you can support by science.

, however I still don't know what do we mean by "universe", is it the space that we know, or it also inclues beyond space "Vacume !".

So you are making a definitive statement about something you can't even define. Now that's REALLY scientific.

What do you call the "No Space/No Time" before the big bang?!

I don't call it anything since there is no evidence that there was such a thing and it is not part of the big bang theory

 

[thorium1010]

But there is no such thing as infinity in physics !

Infinity is a really very very large number no one can reach. Its a concept used in math and physics. Nobody knows the real size of the universe. It is really really large. Like mathman said finite or infinite is a open question.

 

[Drakkith]

One cannot probe anything tangible is infinite in size, extent, or count. It would take an unending amount of time. However the concept of infinity does exist.

 

[andrewmh]

the big bang does not prove that there is no boundary to the universe. the expansion of space isn't the physical expansion of acquiring more territory that we experience here on earth. the big bang occurred everywhere at once.

and there can be an infinity. if you follow these two patterns you will notice that they will go on forever
1 2 3 4 5 6 7...
2 4 6 8 10 12...
divide them and you still get a number yet they are both infinitely large.

to add to the idea of no space or time before the big bang, well you pretty much said it. there was no time. kind of a hard thought for human logic but time started at t=0 so yes, time does have a beginning.

plus... at the end of the day, the big bang is still a theory =P

 

[haruspex]

the big bang does not prove that there is no boundary to the universe.

I can't find a post claiming it does. OTOH, does anyone think it does have a boundary?

and there can be an infinity. if you follow these two patterns you will notice that they will go on forever
1 2 3 4 5 6 7...
2 4 6 8 10 12...
divide them and you still get a number yet they are both infinitely large.

But those are not infinities in the physical world, just in mathematical theory.

 

[Chronos]

Er, maybe. That's my answer and I'm sticking to it.

 

[Algren]

I did not ask what you think, I asked what you can support by science.So you are making a definitive statement about something you can't even define. Now that's REALLY scientific.I don't call it anything since there is no evidence that there was such a thing and it is not part of the big bang theory

No offense, but that's not helping at all.

Acc. to me, since light is the fastest thing, then you can define an 'energy & mass' boundary, beyond which only those things lie which existed before the big bang (if anything did). But you can't define a boundary, neither to space, nor to the universe.

to add to the idea of no space or time before the big bang, well you pretty much said it. there was no time. kind of a hard thought for human logic but time started at t=0 so yes, time does have a beginning.

There is a logic behind the beginning of time. Any events which occurred before the big bang does not affect us or the universe today. There is no need to assign these useless and unknown events with a time. Thats why we have BIG BANG occurred at t=0;

 

[Ken G]

I think there is even some confusion here about the kinds of questions that science is able to answer. We actually don't use science to answer questions like "is the universe finite or infinite", we just use it to address questions like "is the universe finite." The answer to that question is, "we have no scientific evidence that the universe is finite." That's it, that's all we can use science to say. This is not evidence that the universe is infinite, such a thing is not likely to even be possible to obtain. Since absence of evidence is not evidence of absence, we simply cannot use science to say anything at all about whether or not the universe is finite in size (in comoving coordinates, etc.), we can only say we have no evidence that it is finite. Why must we always try to use science for more than it is intended or appropriate?

 

[haruspex]

The answer to that question is, "we have no scientific evidence that the universe is finite." That's it, that's all we can use science to say. /QUOTE]

I think we can go a little further than that. Many/most people would assume that if space has no boundaries then it must be infinite in volume. Science can be used to produce models, consistent with physics as far as is known, in which space can be finite yet unbounded. There may even be implications of such models which could be tested.

 

[shreyakmath]

The universe is finite but with no boundary. It is similar to a bubble or sphere

 

[Ken G]

I think we can go a little further than that. Many/most people would assume that if space has no boundaries then it must be infinite in volume.

It's not terribly relevant, but that doesn't follow. Space could curve back on itself, have finite volume, and still have no boundaries. But the real issue here is, despite looking very hard (and quite possibly as hard as we can ever look), we have no evidence that it does have boundaries, nor do we have any evidence that it does not have boundaries, nor do we have any evidence that it curls back on itself, nor do we have any evidence that it does not curl back on itself. All we know is, what we see looks flat, and we have no idea how long it stays looking flat. That's it, that's the scientific evidence in its entirety.

Science can be used to produce models, consistent with physics as far as is known, in which space can be finite yet unbounded. There may even be implications of such models which could be tested.

But making and testing models has nothing to do with answering the OP question. The models we make are intended as idealizations, and the standard idealization is that of a flat infinite universe. That model works quite well. Is that evidence that the universe really is flat and infinite? Of course not. If I am digging a foundation for my house, I'm certainly going to use a model that the surface of the Earth is flat and infinite (in that I will certainly not model any curvature of the Earth), and it will work great for digging my foundation, but I'm never going to conclude that any of this is evidence that the Earth really is flat and infinite.

 

[Ken G]

The universe is finite but with no boundary. It is similar to a bubble or sphere

There is zero evidence that this is the case, and there is also zero evidence that this is not the case. And humanity should be prepared for the possibility that this situation will never change for us, as it seems quite likely at present. Even if efforts to detect a tiny spatial curvature do eventually succeed, it won't require that the universe maintains that same curvature everywhere, that will simply be an idealization of the model, like any other idealization of any other model. It will never be testable as fact, we pretty much already know this.

 

[haruspex]

... that doesn't follow. Space could curve back on itself, have finite volume, and still have no boundaries.

Yes, that's the point I was making.

nor do we have any evidence that it curls back on itself,

I'm far from expert in this area, but my understanding is that General Relativity posits a "flat" spacetime, but a finite, curved space, with a compensating curvature in time.
If so, and if you accept evidence for GR, that is surely evidence for a finite universe.
I would also have thought that an infinite universe was inconsistent with the Big Bang model, and there is much evidence for that.
You seem to be demanding much more direct evidence.

But making and testing models has nothing to do with answering the OP question.

I disagree. The question was "Does it have boundaries? Is it finite?" Establishing that 'finite without boundaries' cannot be ruled out is a partial answer.

 

[Light Bearer]

Oh? Can you prove that? Do you have an accredited references to back up such a categorical statement?

lolz

 

[Ken G]

I'm far from expert in this area, but my understanding is that General Relativity posits a "flat" spacetime, but a finite, curved space, with a compensating curvature in time.

No, GR says that in comoving-frame coordinates (which is what is generally used in cosmology to talk about what the universe as a whole is doing), all the observed curvature due to gravity is in the time dimension (associated with cosmological redshifts), none is in the spatial dimension. We say the universe is "spatially flat" in this sense. The observations cannot rule out some small spatial curvature, but they can rule out the idea that the universe curves back on itself over the range that we can observe or in some way test our inferences about-- and of course we have no idea what it does beyond that range. Even if we do detect some small spatial curvature, it would not require that this curvature is maintained beyond what we can observe-- the cosmological principle applies to explanations of what we actually observe, it is not a philosophical claim about what we cannot observe.

I would also have thought that an infinite universe was inconsistent with the Big Bang model, and there is much evidence for that.

No, the Big Bang model includes neither finiteness nor spatial curvature at present. So the model is one of an infinite universe. However, the model need not make any claims that this is actually true, it just means we have no reason to model finiteness of the universe.

I disagree. The question was "Does it have boundaries? Is it finite?" Establishing that 'finite without boundaries' cannot be ruled out is a partial answer.

I said it could not be ruled out. I also said the alternative could not be ruled out. In fact there is no evidence at all either way. When there is no evidence in favor of a proposition, nor evidence against it, it doesn't leave you with a whole lot more to say, which is the point.

 

[twofish-quant]

Even if we do detect some small spatial curvature, it would not require that this curvature is maintained beyond what we can observe-- the cosmological principle applies to explanations of what we actually observe, it is not a philosophical claim about what we cannot observe.

But CMB power spectrums can and do constrain large scale anisotropy. We can directly measure what's in our bubble, we can infer things for some distance outward.

Also, if we do detect small scale curvature, this is going to very strongly constrain the details of inflation and we can use that to infer a lot of stuff.

No, the Big Bang model includes neither finiteness nor spatial curvature at present. So the model is one of an infinite universe.

This is incorrect. LCDM doesn't require finiteness, but it doesn't exclude it. Also whether the current model allows for a finite universe is an observational equation that changes from moment to moment. Before the discovery of dark energy, the amount of dark matter in the universe was clearly insufficient to close the universe so there was a period of a few years in which the preferred model was infinite and negatively curved.

Then we have dark energy and everything changed.

When there is no evidence in favor of a proposition, nor evidence against it, it doesn't leave you with a whole lot more to say, which is the point.

At that point you step back and figure out what you need to find out to constrain what you know. If you don't know, the next question is what do you need to do to find out.

 

[twofish-quant]

I'm far from expert in this area, but my understanding is that General Relativity posits a "flat" spacetime, but a finite, curved space, with a compensating curvature in time.

Nope. Everything is curved. Also you can have negative curvature which gives you something that looks like a saddle, and negative curvature turns out to be infinite.

 

[twofish-quant]

There is a logic behind the beginning of time. Any events which occurred before the big bang does not affect us or the universe today. There is no need to assign these useless and unknown events with a time. Thats why we have BIG BANG occurred at t=0;

That's false. Unknown does not mean unknownable and there are several promising avenues of inquiry for what happened before t=0. What happens before t=0 can potentially affect things like the CMB anisotropy.

 

[twofish-quant]

Even if efforts to detect a tiny spatial curvature do eventually succeed, it won't require that the universe maintains that same curvature everywhere, that will simply be an idealization of the model, like any other idealization of any other model. It will never be testable as fact, we pretty much already know this.

You give up too easily.

Absence of evidence is not evidence of absence.
Unknown does not mean unknowable.

There's a lot of data from CMB observations, and that can be used to strongly constrain possible models.

 

[Ken G]

But CMB power spectrums can and do constrain large scale anisotropy. We can directly measure what's in our bubble, we can infer things for some distance outward.

Right, and what we find, when we do that, is zero evidence of any spatial curvature, which is consistent with inflation. If inflation is correct, this will always be true, no matter how good our observations get.

Also, if we do detect small scale curvature, this is going to very strongly constrain the details of inflation and we can use that to infer a lot of stuff.

If we detect that, you can throw away inflation completely!

This is incorrect. LCDM doesn't require finiteness, but it doesn't exclude it.

You don't see what I'm saying. LCDM is not a statement about what the universe is really like, it is a good model of the universe. That's a rather important distinction, and cuts right to the heart of what physics and astronomy does! What's more, LCDM is flat, and invokes the cosmological principle, and so it is a model of an infinite universe. Of course these are idealizations, physics deals exclusively in idealizations, it makes models. As I said, that does not mean it asserts the universe is infinite, it means it is an infinite model of the universe. Which is just precisely what it is. Newtonian physics was never an assertion that the universe is deterministic, it was always a deterministic model of the universe, which is quite different.

What's more, if inflation is correct, and the cosmological principle continues to be the key simplification in the Big Bang model, then this will always be true-- our model of the universe will always be flat and infinite. This is just plain fact, the logic is straightforward.

Also whether the current model allows for a finite universe is an observational equation that changes from moment to moment.

I have never been talking about "what the current model allows." The current model allows for unicorns, space aliens, and teleportation beams. But none of those are included in the current model, because there is no need for them, and no evidence in favor of them. Again this is a rather important distinction.

Now I agree that unicorns are not as likely as the possibility that inflation or the cosmological principle will someday be deemed incorrect and get replaced, but no one has that crystal ball. I'm talking about the evidence that exists today, and the models we build based on that evidence. And that evidence is used to build flat models of an infinite universe-- with no claim whatsoever that this is the truth of the matter, it is just our best model. Physics never gets to know the truth of the matter, all it ever gets is its best models, and they are always provisional on what we know at the time. So it was with Ptolemy, Copernicus, Galileo, Newton, Einstein... etc.

Before the discovery of dark energy, the amount of dark matter in the universe was clearly insufficient to close the universe so there was a period of a few years in which the preferred model was infinite and negatively curved.

Then we have dark energy and everything changed.

Right-- and what got changed is we got a flat model! Which is what I have been talking about all along.

 

[twofish-quant]

Right, and what we find, when we do that, is zero evidence of any spatial curvature, which is consistent with inflation. If inflation is correct, this will always be true, no matter how good our observations get.

This is also false. The current data is consistent with zero *average* spatial curvature. However from the CMB data we can calculate the variation of spatial curvature around the average and that number is *NOT* zero.

see http://ned.ipac.caltech.edu/level5/Sept05/Hu/Hu3.html for the theory

and the WMAP for the curvature amplitude.

So the WMAP results pretty clearly show that there is curvature, whether it averages out to zero is another question.

If we detect that, you can throw away inflation completely!

Did you read Guth's paper? This isn't true.

Inflation is a general mechanism to increase flatness and solve the horizon problem. If we find a non-zero curvature then it kills some versions of inflation but doesn't kill the whole framework.

Let me point out that until 1998, the best cosmological data suggested negative curvature and that hardly killed in the inflationary scenario.

What's more, LCDM is flat, and invokes the cosmological principle, and so it is a model of an infinite universe.

That's false, LCDM is a priori *NOT* a flat model. You can set the parameters to get a flat model. Also even if you set the parameters so that the *average* curvature is zero in order to reproduce the CMB spectrum you need to include first order curvature fluctuations.

I don't want to get to deep into philosophy, because I disagree with you on two factual issues, and it's sort of pointless to get deep into philosophy without resolving the factual disagreements.

1) Inflation doesn't not necessarily imply unmeasurably small cosmological constants
2) LCDM does not assume flatness. You can get a version of LCDM to work with current observations by assuming average flatness, but even where you do that, LCDM assumes deviations from flatness.

Also, I'm interested in where you are getting your information since it's wrong. I'm keen to stamp out misinformation, so I'd be interested in finding out where the misinformation came from (and in case the answer is Wikipedia, i changed some of the pages recently to remove the incorrect statement that LCDM assumes flatness).

 

[twofish-quant]

I'm talking about the evidence that exists today, and the models we build based on that evidence. And that evidence is used to build flat models of an infinite universe-- with no claim whatsoever that this is the truth of the matter, it is just our best model.

One other thing to note is that before the discovery of "dark energy" in 1998, the best available model (CDM) resulted in a negative curvature model of the universe. It's only after you add dark energy that you get something like a flat universe.

Which is why I dispute your statement that a flat universe is *required* for inflation. As of 1995, it was believed that we didn't live in a flat universe, because without dark energy flatness is excluded to pretty high certainty, but that didn't kill off inflation.

Right-- and what got changed is we got a flat model! Which is what I have been talking about all along.

And I'm saying this is false. If you look at the parameterizations for WMAP, you'll find that the model that they use to calculate observational constraints is not flat.

 

[Ken G]

One other thing to note is that before the discovery of "dark energy" in 1998, the best available model (CDM) resulted in a negative curvature model of the universe. It's only after you add dark energy that you get something like a flat universe.

Right, but that's exactly why the CDM model was uniformly rejected by just about everyone. That is in complete contrast with the models of today, with which we often hear the phrase "precision cosmology", and has been related to several Nobel prizes.

Which is why I dispute your statement that a flat universe is *required* for inflation. As of 1995, it was believed that we didn't live in a flat universe, because without dark energy flatness is excluded to pretty high certainty, but that didn't kill off inflation.

No, that's not true. I was an astronomer in 1995 also, and few thought the universe was not flat, they thought the model was wrong. That's also why there were no Nobel prizes awarded for the CDM model. Indeed, it was considered a huge problem that the flatness parameter came out 0.3, which was way too close to 1 to not be 1 (a flatness less than 1 gets exponentially less flat with time, so to be 0.3 now, it would have had to have been extremely close to 1 in the past, but still strangely different from 1). Even in 1995, inflation was commonly taught, and it was widely expected that the flatness should be 1. The missing energy was just considered a paradox that no one knew how to solve, but made people worried that we were missing something really crucial. Today that is not the sentiment, hence all the Nobel prizes, though of course there are plenty of people still not completely happy with dark energy, and that's why we have some people claiming that you need multiverses to explain it. I'm not banking on that approach myself, however, I just think we are still missing some key physics, but the models of the universe will still be flat (except for local fluctuations with no global significance), and we will just never get to know anything beyond that for the simple reason that we cannot look.

And I'm saying this is false. If you look at the parameterizations for WMAP, you'll find that the model that they use to calculate observational constraints is not flat.

I'm not sure where you get that, but it is incorrect. See the WMAP website at http://map.gsfc.nasa.gov/universe/uni_shape.html , where we find quotes like:
"If the density of the universe exactly equals the critical density, then the geometry of the universe is flat like a sheet of paper, and infinite in extent. The simplest version of the inflationary theory, an extension of the Big Bang theory, predicts that density of the universe is very close to the critical density, and that the geometry of the universe is flat, like a sheet of paper."
and:
"We now know that the universe is flat with only a 0.5% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe."
Which is what I have been saying.

 

[Ken G]

Also, I'm interested in where you are getting your information since it's wrong.

It comes from modern astronomy textbooks, and websites like the WMAP website I quoted above. So, where are you getting your misinformation, given that you are "keen" to stamp it out?

 

[twofish-quant]

It comes from modern astronomy textbooks, and websites like the WMAP website I quoted above.

Which textbooks? Graduate or undergraduate?

The WMAP website oversimplifies things. I'll e-mail the maintainers of the site to get it changed.

So, where are you getting your misinformation, given that you are "keen" to stamp it out?

1) from the graduate courses that I took in cosmology when I got my Ph.D. in astrophysics

2) from talking with cosmologists and supernova people, include one of the lead co-authors of the WMAP paper, one person that was a co-author on the supernova Ia investigation papers, and one person that has a Nobel prize in physics.

 

[Ken G]

Which textbooks? Graduate or undergraduate?

Either one. Just not textbooks expressly designed to investigate speculative areas of astronomy. Such books always appear at the fringes of any science, they are certainly not quackery, but they are usually forgetten in a few decades-- such is the nature of controversial speculation. No doubt there are graduate textbooks on MOND, on loop quantum gravity, and on microscopic black holes.

The WMAP website oversimplifies things. I'll e-mail the maintainers of the site to get it changed.

Good luck with that, I'm sure they'll be thrilled to have your expertise weighing in.

1) from the graduate courses that I took in cosmology when I got my Ph.D. in astrophysics

They told you that eternal inflation is a mainstream consensus idea? I doubt that strongly.

2) from talking with cosmologists and supernova people, include one of the lead co-authors of the WMAP paper, one person that was a co-author on the supernova Ia investigation papers, and one person that has a Nobel prize in physics.

I don't see any quotes from them in your argument. What are you claiming they said, and why don't you think it is making it to the WMAP website?

 

[twofish-quant]

Either one. Just not textbooks expressly designed to investigate speculative areas of astronomy.

It would help if you gave me some authors.

No doubt there are graduate textbooks on MOND, on loop quantum gravity and on microscopic black holes.

Not really. MOND and LQC are changing too quickly for there to be much in the way of textbooks, so you end up with review papers and paper collections. Microscopic black holes are very interested from a theory standpoint, but there isn't much to say about them.

Good luck with that, I'm sure they'll be thrilled to have your expertise weighing in.

Well yes.

They told you that eternal inflation is a mainstream consensus idea? I doubt that strongly.

No they told me that

1) inflation doesn't require zero curvature
2) the current model of cosmology doesn't assume flatness

I don't see any quotes from them in your argument.

Give me a few days. If I can get you a personal email from one of the three people confirming my points, will you concede the argument? Also, I want to define the question, because I don't want to get into a situation where I bug someone who is busy, get an e-mail, and then you argue that the e-mail doesn't refute your point.

Conversely if you concede those two points now, you save me the effort of writing an e-mail.

What are you claiming they said, and why don't you think it is making it to the WMAP website?

1) inflation doesn't require zero curvature
2) the current model of cosmology doesn't assume flatness

Because the WMAP website was intended for non-technical people, and they simplify a lot of stuff in ways that could be misleading. That's why I'd prefer a reference to something stronger. If you have a citation to a paper in ApJ or a graduate textbook that argues that inflation is inconsistent with non-zero curvature, that would be different than a public affairs website.

 

[Ken G]

Give me a few days. If I can get you a personal email from one of the three people confirming my points, will you concede the argument? Also, I want to define the question, because I don't want to get into a situation where I bug someone who is busy, get an e-mail, and then you argue that the e-mail doesn't refute your point.

Obviously, it is very important to detail the issue correctly. The way you have paraphrased my arguments makes me doubt your version would have much resemblance. For one thing, you insist that I'm claiming that inflation implies the universe is flat. Of course it does no such thing, inflation is a model, it does not constrain the universe, rather the universe, in concert with the goals and demonstrable benefits of science, constrains the model. What I'm actually saying is threefold:

1) For inflation to continue to be regarded as a good model of what really happened in our universe, with no need for anthropic thinking, then curvature must never be detected, and conversely, if curvature is detected, then inflationary models will be up to their ears in anthropic justifications, so much so that much of their original purpose (to escape anthropic thinking) will be lost.

2) The current best model of the universe is a flat, infinite model that obeys the cosmological principle. Occam's razor contributes significantly to making this our best model. Its success is by no means a claim that the universe is actually flat or infinite, for indeed no model can ever make such a claim, given that we cannot see far enough to check it, and never will.

3) The question "is the universe infinite" could never be answered "yes" by any scientific means imaginable. It could only be answered "no", and we already know it cannot be so answered, because we already know we cannot see the limit of the universe. Even if we detect some tiny positive curvature, it would only mean that our best model was now a closed finite model, and again by Occam's razor-- not by any testable claim on the actual geometry of the universe that we cannot see. The best model is never a claim on things that observations are moot about, such things are adopted in the model purely based on Occam's razor. We must stop pretending that science can determine truths even after we have discovered that the observations cannot.

These are the three points I have repeated over and over, and I have never said, or thought, anything else of importance to this discussion. Anyone whose opinion you'd like to solicit on those three points would be more than welcome, indeed quite informative. But the way you have characterized my points is completely inaccurate, and framing the issue as you put it above would have no value whatsoever.

 

[twofish-quant]

1) For inflation to continue to be regarded as a good model of what really happened in our universe, with no need for anthropic thinking, then curvature must never be detected, and conversely, if curvature is detected, then inflationary models will be up to their ears in anthropic justifications, so much so that much of their original purpose (to escape anthropic thinking) will be lost.

And I strongly disagree. If it turns out that there is curvature that imposes a natural scale to the inflation. At that point we can look at the details of the inflation mechanism to see what physics would cause inflation to stop that that scale. For example, if inflation stops when some energy level reaches Planck's constant, then whatever stops inflation could be some quantum tunneling effect.

In physics this is called "hand waving" but it's a useful technique.

2) The current best model of the universe is a flat, infinite model that obeys the cosmological principle.

Again this is incorrect. Cosmologists do not assume that the universe is flat.

Occam's razor contributes significantly to making this our best model.

I'd argue that it doesn't. Where we don't add a term, there are reasons why a term is avoided. Occam's razor tends to be overused as a justification, and it's not that really useful in complex systems.

3) The question "is the universe infinite" could never be answered "yes" by any scientific means imaginable.

I think that you are limiting yourself. I *might* agree to the statement, if you put "currently imaginable" in that statement. Also, the statement of "assuming the universe is isotropic, must it also be infinite?" is something that *can* be answered yes or no.

We must stop pretending that science can determine truths even after we have discovered that the observations cannot.

But this is "proof by lack of imagination." Unknown is not unknowable, and if you want to convince me that something is "unknownable" then you have to give some quasi-mathematical proof of it. Then you run into the issue of whether something is unknowable is itself unknowable.

 

[twofish-quant]

Also just to clarify. Is assertion 1) something you got from someone else or something you made up. It makes a difference between if it's something you got from someone else, then it's easier if you just put a link to where ever you got the idea.

Also one other point is that neither 1) or 2) is "mainstream cosmology."

 

[marcus]

Ken I like some of your posts on other threads e.g. the multiverse issue. thoughtful and cogent. In this case your point #3 is extremely well taken. We don't expect scientists to claim X is the absolute truth. We are happy if they offer the simplest best fit model that has been devised so far and the most reliable model so far for predicting future observations.

So, as you say in point #3 if some positive curvature is discovered (with 95% certainty say) then the simplest best fit model becomes spatially finite. But like any scientific finding that would be provisional and no one can predict the future discoveries. The model might be revised down the road a ways.

That said, you might want to relax your points #1 and #2. I've always understood inflation as having leveled things out enough to be consistent with what we see today. Inflation is consistent with some slight residual curvature.

The treatment of inflation in Loop cosmology does not require fine-tuning and makes an adequate inflation era highly probable. It is consistent with some curvature and if curvature were detected would not bring on the "anthropery" bogeyman. Whether you get threatened by anthopery is to some extent model dependent. Some recent Ashtekar papers about inflation. So point #1 is not terribly firm.

Point #2 is a rather one-sided invocation of Occam, I think. Some people would put Occam on the side of a spatially finite universe, other things equal. I find the finite volume case easier to imagine, simpler. The infinite case with its infinite amount of matter and energy is quite a stretch to imagine. Uniformly distributed too! Infinite energy homogeneously distributed throughout infinite volume!

What you think Occam tells you is to some extent a matter of taste and community consensus. One doesn't want to be too dogmatic about what Occam says is "best". I think anyway.

There's a lot of good in what you say, here and elsewhere, but I think you might relax slightly on points 1 and 2 here.

... What I'm actually saying is threefold:

1) For inflation to continue to be regarded as a good model of what really happened in our universe, with no need for anthropic thinking, then curvature must never be detected, and conversely, if curvature is detected, then inflationary models will be up to their ears in anthropic justifications, so much so that much of their original purpose (to escape anthropic thinking) will be lost.

2) The current best model of the universe is a flat, infinite model that obeys the cosmological principle. Occam's razor contributes significantly to making this our best model. Its success is by no means a claim that the universe is actually flat or infinite, for indeed no model can ever make such a claim, given that we cannot see far enough to check it, and never will.

3) The question "is the universe infinite" could never be answered "yes" by any scientific means imaginable. It could only be answered "no", and we already know it cannot be so answered, because we already know we cannot see the limit of the universe. Even if we detect some tiny positive curvature, it would only mean that our best model was now a closed finite model, and again by Occam's razor-- not by any testable claim on the actual geometry of the universe that we cannot see. The best model is never a claim on things that observations are moot about, such things are adopted in the model purely based on Occam's razor. We must stop pretending that science can determine truths even after we have discovered that the observations cannot.

These are the three points I have repeated over and over, and I have never said, or thought, anything else of importance to this discussion. Anyone whose opinion you'd like to solicit on those three points would be more than welcome, indeed quite informative. But the way you have characterized my points is completely inaccurate, and framing the issue as you put it above would have no value whatsoever.

 

[Ken G]

That said, you might want to relax your points #1 and #2. I've always understood inflation as having leveled things out enough to be consistent with what we see today. Inflation is consistent with some slight residual curvature.

Here's the problem. You have an inflation model, and it has some parameter in it, perhaps the shape of some scalar potential function. You then look at the curvature today, run your GR backward until inflation ends, and try to match up what you get. Certainly you can take any current curvature, no matter how close to flat it is, and you'll get an answer to this exercise. The issue is what is the "size of the target" you are trying to match. If current curvature is not detectable at the, say, .0001 level, then you have a vast range of possible curvatures at the end of inflation, you just map from .0001, to 0, all the way back, and what you get is a hugely wide range of possible curvatures at the end of inflation. Now you have some hope that a plausible inflation model, that is consistent with other established physics, will "hit the target."

Now imagine some observation was just done that detects spatial curvature, say it's in the range .0001 to .0002. Play the same game, map that backward to the end of inflation, and now you have only a factor of 2 in parameter space-- that's the size of the target you have to "hit" with your inflation model. twofish-quant is saying that he has the hope that a plausible inflation scenario that is based on some atomic scale will rather magically hit this target. I'm saying that's pure hope, but at least it's a plausible hope if you have orders of magnitude of possible curvatures that fit with the modern observations. But let's say that a miracle occurs and a natural-sounding inflation model with some built-in established subatomic scale hits the target with finite curvature today. That will certainly seem like a convincing case for that inflation model, a slam dunk even.

But look at the cost we've had to pay-- first of all, we seem to have gotten really lucky to have hit the target, but that's what we are using to justify faith in our model. What's worse is, we now have to wonder why that subatomic scale happens to be set just to hit that tiny range, out of all the orders of magnitude of possiblities for a subatomic scale, so as to just barely generate measurable curvature today! The inflation model seems correct, even undeniable, but it's lost its main purpose: to be able to see the universe as not special or finely tuned. We'd be right back to anthropic reasoning-- the subatomic scale must be coming out that way so as to create a universe with small but measurable curvature because we couldn't exist in all the other more generic universes where that was not the case.

The treatment of inflation in Loop cosmology does not require fine-tuning and makes an adequate inflation era highly probable. It is consistent with some curvature and if curvature were detected would not bring on the "anthropery" bogeyman.

But I think it would. Look at it this way. Take the model you have in mind, and partition its possible parameters into two sets-- the set that leads to unobservable curvature, and the set that leads to small but observable curvature. Of course throw out the set that we've already falsified because it leads to huge curvature. Really do this, it should be easy enough with whatever model you have in mind. Now ask a simple question-- what is the relative measure of those two sets? Is it not true that the unobservable curvature parameter set has vastly larger measure than the observable curvature set? So how is it not fine tuned if we detect curvature tomorrow? How do you answer the question: why that parameter set and not the other parameter set, if the other one was orders of magnitude larger?

Point #2 is a rather one-sided invocation of Occam, I think. Some people would put Occam on the side of a spatially finite universe, other things equal.

It is certainly true that Occam's razor is never clear-cut, but if you just look purely at the model, with no extraneous baggage that says the model is supposed to be the actual reality, then it is clear enough that a model with a non-arbitrary value for the flatness (i.e., flat) is simpler than one with an arbitrarily chosen value of curvature (how do you even give a value to it?). Also, it is much easier to use for doing calculations, which is the key issue I would say.

I find the finite volume case easier to imagine, simpler.

Simplicity of imagining is a different flavor of Occam's razor, it's hard to say if a "best model" is the one that has the fewest arbitrarily chosen parameters (like flat versus some essentially randomly chosen curvature that is not refuted by observation), or the one that is "easiest to picture." My point is that once you are on board with point #3, you are relieved of any philosophical issues with an infinite universe, because you are not claiming the universe is infinite-- you are just fitting what we see to a flat model, like fitting a tangent plane to a manifold where you cannot measure any deviation between the two. The tangent plane is mathematically non-arbitrary, but it is hard to picture because it goes off to infinity in all directions. If we saw that as a bad thing, we could certainly do all of calculus to any precision with circles and spheres of small enough curvature, but we don't, we have lines and planes, because they are mathematically simpler, though harder to picture.

 

[Ken G]

Also just to clarify. Is assertion 1) something you got from someone else or something you made up.

Neither. It comes from me, but it stems from a logical argument. I summarized that argument again just above. So if you want to critique it, you do better finding an actual flaw in the logic.

Also one other point is that neither 1) or 2) is "mainstream cosmology."

You don't seem to even understand what I'm saying with 1) or 2), so I'm suspicious of your judgements of these points. For example, you insist on claiming that I have said that cosmologists assume the universe is flat. That is so completely different from anything I've said, or even thought, that I have no idea where you are even getting that from, but you can't be reading very carefully.

 

[twofish-quant]

Now imagine some observation was just done that detects spatial curvature, say it's in the range .0001 to .0002. Play the same game, map that backward to the end of inflation, and now you have only a factor of 2 in parameter space

If the curvature is positive then at some point in the life of the universe it will take all values from 1e-16 to infinity. We happen to catch it at 0.001, but wait a few billion years and it will be 0.002. Then 0.3, then 0.5, then 2, then 1000, then at some point dark energy takes over and it goes down again.

twofish-quant is saying that he has the hope that a plausible inflation scenario that is based on some atomic scale will rather magically hit this target.

If there is *any* curvature, no matter how small, then the universe at some point in it's life will take all values between that small curvature and infinity.

But look at the cost we've had to pay-- first of all, we seem to have gotten really lucky to have hit the target, but that's what we are using to justify faith in our model.

No we don't. It's not a matter of hitting a target. As long as the inflation ends with *any* positive curvature, then things will work. It doesn't matter whether the minimum curvature is 10^-32, 10^-50, or 10^-100. Once the universe starts expanding from *any* small curvature, it will take *all* values between that small number and some limit at which when dark energy takes over.

So it doesn't *matter* what the minimum curvature is. It could be *any* number below observation. If it is 10^-100, it will eventually blow up to be 0.001. If it is 10^-32, it will eventually blow up to be 0.001. The only "magic" is that we see it at 0.001 rather than 0.002 or 0.01 which is what we will see if we wait a few billion years.

But I think it would. Look at it this way. Take the model you have in mind, and partition its possible parameters into two sets-- the set that leads to unobservable curvature, and the set that leads to small but observable curvature. Of course throw out the set that we've already falsified because it leads to huge curvature. Really do this, it should be easy enough with whatever model you have in mind. Now ask a simple question-- what is the relative measure of those two sets? Is it not true that the unobservable curvature parameter set has vastly larger measure than the observable curvature set? So how is it not fine tuned if we detect curvature tomorrow?

You are making quasi-anthropic arguments which I dislike. And no. It doesn't work that way. Suppose you end inflation with a undetectable positive curvature. This positive curvature will take all values from 10^-whatever and some large number at which you have dark energy take over.

Instead of taking multiple universes, let's just take one.

Now let's take a random point in the life of a universe with a positive curvature.

You have inflation and it reduces the curvature to some random small number. Now let's evolve the universe. It turns out that for most of the life of the universe, you will have a detectable curvature. If inflation ends with *any* positive curvature no matter how small, then at some point in the life of the universe, that curvature will take every positive value. So someone at some point will wonder why they observe 0.001, someone else will wonder why they observe 0.3, someone else will wonder they observe 1.0, and there is nothing to explain. You observe X, because you happen to be at the stage of the universe where you see X.

My point is that once you are on board with point #3, you are relieved of any philosophical issues with an infinite universe, because you are not claiming the universe is infinite-- you are just fitting what we see to a flat model, like fitting a tangent plane to a manifold where you cannot measure any deviation between the two.

Philosophy would be easy if we didn't have to worry about observations.

 

[twofish-quant]

Neither. It comes from me, but it stems from a logical argument. I summarized that argument again just above. So if you want to critique it, you do better finding an actual flaw in the logic.

If it comes from someone else, then it's likely that it's already been critiqued and I can pop up google and replay the conversation.

For example, you insist on claiming that I have said that cosmologists assume the universe is flat.

You are saying that the best model used by cosmologists assumes a flat universe, and I'm saying that's not the case.

That is so completely different from anything I've said, or even thought, that I have no idea where you are even getting that from, but you can't be reading very carefully.

Communication is difficult, and if you aren't making that assertion, then what assertion you are making. You have said that LCDM assumes a flat universe, and that's false.

 

[Ken G]

If the curvature is positive then at some point in the life of the universe it will take all values from 1e-16 to infinity. We happen to catch it at 0.001, but wait a few billion years and it will be 0.002. Then 0.3, then 0.5, then 2, then 1000, then at some point dark energy takes over and it goes down again.

But that's just it, the dark energy has already taken over. So we are pretty much at the curvature "peak" right now. That's the problem with a peak curvature that just happens to be what we can barely measure, why on Earth would life come along at just the time when it can barely measure the curvature? That's the "fine tuning problem" that you would be staring at if curvature is detected, and that's what would steal most of the wind from inflation's sails.

If there is *any* curvature, no matter how small, then the universe at some point in it's life will take all values between that small curvature and infinity.

No, not with dark energy.

Once the universe starts expanding from *any* small curvature, it will take *all* values between that small number and some limit at which when dark energy takes over.

Exactly, and if curvature is detected, then we will have the fine tuning problem that dark energy is taking over at exactly the point when the curvature is barely detectable by intelligent life. That's just the fine tuning that Weinberg argued is evidence for a multiverse, in relation to the amount of dark energy-- you would be in the exact same boat, but now in regard to curvature instead. You would need an anthropic argument to escape the appearance of fine tuning, and it would have to magically be consistent with the same anthropic argument that is supposed to be what let's dark energy be 10¹⁰⁰ time weaker than it "ought to" be. If we reject this is an escape hatch for the inflation theory, then we have no explanation for why the universe has a sense of humor that it will just let us glimpse the curvature before dark energy washes it away.

Instead of taking multiple universes, let's just take one.

I agree completely, I don't think resorting to multiple universes is a fair way to make a theory seem palatable or plausible. That's exactly why I claim any inflation proponent should be hoping we never detect curvature, and indeed, should probably even be confident we never will. There's just no reason for the parameters of a working inflationary model to be so well perched at that arbitrary tipping point that would suddenly seem very special indeed.

You have inflation and it reduces the curvature to some random small number. Now let's evolve the universe. It turns out that for most of the life of the universe, you will have a detectable curvature.

I don't agree, I think that for the vast majority of ways to set up that universe, the curvature will remain way too small to detect, because the one-two punch of inflation and dark energy will insure that. That holds whether you imagine a cosmological constant or a quintessence-type continuous inflation. You have to really fine tune the combination of inflation and dark energy to both have a universe that inflates enough to be anything like what we see (and, dare I say it, to support life), but still leave a window for detectable curvature for a few billion years out of that vastly aging universe-- exactly when life comes along. That's the problem I've been talking about, this bizarre "glimpse of curvature" phenomenon, which has no "natural" explanation at all, and would sorely tax the whole spirit of using inflation to recover a "natural" feel.

 

[Ken G]

You are saying that the best model used by cosmologists assumes a flat universe, and I'm saying that's not the case.

No, a thousand times no. Not only did I never say that, I bent over backward many times over to stress that is exactly not what I am saying.

Communication is difficult, and if you aren't making that assertion, then what assertion you are making.

Yes, communication is the hardest thing, so let me repeat again what I have been saying. Cosmologists make models, and they make the models only as complicated as necessary to fit the data. The current models that do that are flat, and use the cosmological principle, so they are infinite models, like a derivative is an infinite model of a function even if the function becomes uncertain outside of some compact region. As I've repeated many times now, no such flat and infinite model can say anything at all about the infiniteness of the universe, indeed I stressed several times (there are at least three threads we are debating, so it's hard to keep track of where!) that the question "is the universe infinite" is fundamentally a question that science could never answer in the positive. But science can certainly, and does, make infinite models, if it has no evidence for making them finite. No such model is a claim on what we cannot observe, nor would there ever be any scientific validity in making any claims on such a region.

You have said that LCDM assumes a flat universe, and that's false.

Never said anything like that, nope. I said LCDM is a flat model, which is a totally different claim. It just says the simplest model that fits what we see is a flat infinite universe model, that is not at all "assuming the universe is flat." We don't make assumptions about the universe, we embed assumptions into models, in order to make good models, not in order to use models to make claims on the universe. The logic goes the other way-- observations of the universe inform our models, our models do not inform the universe that is outside the observations we used to make the model.

 

[marcus]

No, a thousand times no. Not only did I never say that, I bent over backward many times over to stress that is exactly not what I am saying. Yes, communication is the hardest thing, so let me repeat again what I have been saying. Cosmologists make models, and they make the models only as complicated as necessary to fit the data. The current models that do that are flat, and use the cosmological principle, so they are infinite models, like a derivative is an infinite model of a function even if the function becomes uncertain outside of some compact region. As I've repeated many times now, no such flat and infinite model can say anything at all about the infiniteness of the universe, indeed I stressed several times (there are at least three threads we are debating, so it's hard to keep track of where!) that the question "is the universe infinite" is fundamentally a question that science could never answer in the positive. But science can certainly, and does, make infinite models, if it has no evidence for making them finite. No such model is a claim on what we cannot observe, nor would there ever be any scientific validity in making any claims on such a region.
Never said anything like that, nope. I said LCDM is a flat model, which is a totally different claim. It just says the simplest model that fits what we see is a flat infinite universe model, that is not at all "assuming the universe is flat." We don't make assumptions about the universe, we embed assumptions into models, in order to make good models, not in order to use models to make claims on the universe. The logic goes the other way-- observations of the universe inform our models, our models do not inform the universe that is outside the observations we used to make the model.

Things are getting clearer. You are not saying that mainstream cosmologists believe the universe is spatially flat, or infinite.

You are claiming that the predominant model in use, the LCDM, comes in only one version and that version is spatially infinite with zero curvature.

If you have never seen a cosmologist use a version of LCDM which has overall slightly positive curvature, then this claim is certainly understandable! It would square with your experience for you to insist that there is only the one version in use, with infinite space and matter.

However my experience is different from yours. I have seen top level cosmologists use different versions of LCDM, and for example, calculate a lower bound for the radius of curvature for the spatially finite positive curved version of LCDM.

You might recall this from the WMAP5 report by Komatsu et al (2010)

In other words, in my experience cosmologists do not jump to premature conclusions, do not gloss over different cases, and instead take the Omega confidence interval very seriously. Since the confidence interval has a substantial range above 1 that necessarily requires a spatial finite (but "nearly" flat) version of LCDM.

I think (if I understand you) we are getting closer to agreement because you are saying that cosmologists do not assume the U is spatially flat and infinite. I agree with you there.
If I understand correctly, you are merely saying that the LCDM model they use (but of course don't assume to be right) has only one version, which is exactly flat and infinite, spatially. And I disagree that there is only one sole model, not a confidence interval of different cases to which the model can be applied.

 

[ViewsofMars]

See the WMAP website at http://map.gsfc.nasa.gov/universe/uni_shape.html , where we find quotes like: [. . .]

and

The WMAP website oversimplifies things. I'll e-mail the maintainers of the site to get it changed.
1) from the graduate courses that I took in cosmology when I got my Ph.D. in astrophysics

2) from talking with cosmologists and supernova people, include one of the lead co-authors of the WMAP paper, one person that was a co-author on the supernova Ia investigation papers, and one person that has a Nobel prize in physics.

Brief comment, twofish-quant, the WMAP website is also used by the Smoot Group - Astrophysics and Cosmology. Might be worth reviewing their website:http://aether.lbl.gov/education.html

Dr. Smoot is also the Director of the Berkeley Center for Cosmological Physics and a winner of a Nobel Prize. I hope that helps with the ongoing discussion.

I have to go digging in my archives for further information I've stored to present to the discussions you are having with Ken on this topic and a few other topics.

 

[Ken G]

Things are getting clearer. You are not saying that mainstream cosmologists believe the universe is spatially flat, or infinite.

Right, most likely they believe almost as many different things as their are cosmologists, and indeed they are welcome to hold any personal beliefs they wish, but believing it wouldn't make it science.

You are claiming that the predominant model in use, the LCDM, comes in only one version and that version is spatially infinite with zero curvature.

There are always many multiple models in use, for a host of reasons, largely around the "buckshot" principle of doing science. But there is also a clear consensus on what is currently regarded as the best model, the model that is often heard in a sentence with "precision cosmology", and it is a model with no reason to include any curvature, so it doesn't. There's always the interplay between consensus and contrariness in science, and nowhere did I ever say that there is only one cosmological model that ever gets looked at-- I said there is one widely regarded best model, and Nobel prizes have been awarded.

If you have never seen a cosmologist use a version of LCDM which has overall slightly positive curvature, then this claim is certainly understandable!

Actually I have seen curved models invoked many times, my point is that none of those models ever gave us the value, the bang for the buck, that the flat model does. Indeed those models can now be seen to be largely a source of unnecessary complication. Almost all cosmology textbooks, for example, start out with the three possible geometries, and go to great lengths describing their differences, only to throw it all away when they come to describing the currently favored model! It's so much wasted overhead. I've no doubt that electromagnetism textbooks after Maxwell went to great lengths describing all the different ways light might operate in different frames if the speed of light was relative to an aether frame, but at some point, they realized that all that overhead was missing a key simplification that drastically simplified the mathematics of doing calculations-- Einstein's postulate. I'm saying flat models in cosmology are another example of just such a drastically beneficial mathematical simplification, to the point that it is becoming more and more apparent that we should embrace that simplification instead of fighting it every step of the way.

However my experience is different from yours. I have seen top level cosmologists use different versions of LCDM, and for example, calculate a lower bound for the radius of curvature for the spatially finite positive curved version of LCDM.

Certainly. And many experiments in the era of Michelson-Morely were aimed at placing an upper bound on how much the speed of light could deviate from c in various frames. But at some point, the mathematical simplicity of a basic unifying postulate overwhelms all that careful overhead, and you just embrace what has been jumping up and down waving its arms at you all the while.

In other words, in my experience cosmologists do not jump to premature conclusions, do not gloss over different cases, and instead take the Omega confidence interval very seriously.

Just as in pre-Einstein days, they took the confidence interval on c very seriously too.

Since the confidence interval has a substantial range above 1 that necessarily requires a spatial finite (but "nearly" flat) version of LCDM.

And what is the confidence interval on c today? It's not infinitely narrow, right? So does that require we have a "very nearly relativistic" version of physics that we also have to bear in mind, and put in every textbook on relativity theory? Models are intended to be simplifications, there's no "conclusions" that are drawn when we adopt one, certainly not that we are announcing that we are convinced the model should suddenly be regarded as "correct," ignoring the fate of all "correct models" for time immemorial. All it means, when we adopt a particular idealization in some model, is that we are tired of doing extraneous and unnecessary work tracking what is much simpler to just remove from the model. We have simply reached the point of diminishing returns for tracking the complexity, relative to just adopting the simpler postulate. I'm saying cosmology is at that point, but it might take it a little while to make the transition.

Edit: let me rephrase that, I'm not trying to tell cosmologists how to do their business, I'm pointing out that we may very well be approaching a time when we need to give very serious consideration to treating the flatness of our models as a physical principle. Note this still does not represent a claim that the universe is actually flat, any more than relativity is a claim that the photon is exactly massless, it is merely a recognition of the value in adopting a particular mathematical simplification in our best models. That is also an accurate description of the theory of relativity, despite how it is often framed in less scientifically careful terms!

 

[ViewsofMars]

Picking up where I left off.

Nature 404, 955-959 (27 April 2000) article:

A flat Universe from high-resolution maps of the cosmic microwave background radiation
P. de Bernardis et al
[. . .]
The blackbody radiation left over from the Big Bang has been transformed by the expansion of the Universe into the nearly isotropic 2.73 K cosmic microwave background. Tiny inhomogeneities in the early Universe left their imprint on the microwave background in the form of small anisotropies in its temperature. These anisotropies contain information about basic cosmological parameters, particularly the total energy density and curvature of the Universe. Here we report the first images of resolved structure in the microwave background anisotropies over a significant part of the sky. Maps at four frequencies clearly distinguish the microwave background from foreground emission. We compute the angular power spectrum of the microwave background, and find a peak at Legendre multipole lpeak = (197 plusminus 6), with an amplitude DeltaT200 = (69 plusminus 8) microK. This is consistent with that expected for cold dark matter models in a flat (euclidean) Universe, as favoured by standard inflationary models.
[. . .]
http://www.nature.com/nature/journal/v404/n6781/full/404955a0.html