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

[AlbertE]

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.

 

[ibysaiyan]

I think the general consensus is that it's shape is similar to a black hole , hyperbolic. Geometry is dependent on which model universe we are speaking of.. there are open/close systems...

P.S: Open system ( hyperbolic) has the following condition : k<1 , on the other hand a closed system (k>1) would collapse back to a singularity over the passage of time (cyclic universe model).

 

[AlbertE]

Ok - but which of my options would it most look like at this point in time - today - if I were able to hold all the matter in my hand in the shape it had come to form.

 

[Whovian]

First of all, this isn't the shape of matter in the universe. This is something topologically equivalent to the shape of space we're talking about. Also, these are just two-dimensional analogies for the shape of three-dimensional space.

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

No.

But, again, let's assume you're wondering what the Universe is topologically equivalent to.

Science does not know?

That's pretty much it, though we have a good amount of evidence that the observable universe is flat.

A donut?

Assuming you're talking about a 3-Torus.

A soccer ball?

A rugby ball/american football?

The previous two are topologically equivalent.

Saturn?

Well, this would be two Universes, one topologically equivalent to a 3-sphere, one topologically equivalent to a ... something.

A spiral galaxy?

Too confused by what exactly you mean. There are a bunch of interpretations of what you said.

 

[AlbertE]

Hi Whovian.

Ok - today - right now - out there - there are galaxies.

If I wrapped the whole lot of them in a big cloth, that cloth would have a shape. Period.

Where am I going wrong :)

 

[Whovian]

The only thing you're getting wrong is assuming you could wrap all of them in a cloth (of course, assuming you could produce a large enough cloth, it would stand up to the enormous amount of energy being blasted into bits of it by GRBs and so on, and you would have an achievable way to wrap up the galaxies, all without disrupting them, but this is a though experiment.) While there is a limit to the size of the Observable Universe (I can't remember it, it was something like 40-something billion Ly,) we have no idea if the Universe itself is infinite. If it is, there's obviously no way to wrap the infinite galaxies up in a cloth.

 

[phinds]

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

That is an unsupportable assumption. It MAY be true but most likely is not. The universe is almost certainly either infinite or finite but unbounded and in either case there is no "shape" such as you are looking for.

 

[AlbertE]

I disagree.

Yup - its a thought experiment - so I have strong and large bits of cloth :)

Ok - thinking along here...

We know the big bang occurred around 13.7? billion years ago.

If this is true - and I believe it to be the case, then unless it expanded at an infinite speed, it must be finite in size - this is not debateable and is absolutely set in stone.

As the above is not debateable, and we are happy with the timescales give or take - then there is no possibility of the matter being unable to form an outer shape.

Therefore there IS an outer shape which is formed by the fastest moving objects (as they are the outer objects).

LOL - still - where is this theory going wrong? I fear my convictions in simplicity are hindering my search!

 

[George Jones]

We know the big bang occurred around 13.7? billion years ago.

If this is true - and I believe it to be the case, then unless it expanded at an infinite speed, it must be finite in size - this is not debateable and is absolutely set in stone.

No, this is wrong. There are many situations to which everyday physical intuition does not apply. The Big Bang was not a place in space from which all matter emerged.

 

[phinds]

unless it expanded at an infinite speed, it must be finite in size - this is not debateable and is absolutely set in stone.

No, as George said, this is totally wrong. It happened everywhere at once, not a some point. You should check out the FAQ sticky in the cosmology section, or try this:

www.phinds.com/balloonanalogy

 

[AlbertE]

Sorry - "what" happened everywhere at once? There was at the beginning of time, no everywhere!

 

[Whovian]

Sorry - "what" happened everywhere at once? There was at the beginning of time, no everywhere!

The Big Bang happened everywhere at once. It did not start at a point and the Universe came into existence as the spherical explosion propagated outward. The Big Bang occurred at every point in space simultaneously.

 

[George Jones]

This may not be completely accurate, but it might be better to think along the lines of

Very good stuff guys.
But it started from a singularity.Which is a single point .Hence a center.

No, a singularity is not necessarily a single point. A singularity is usually more like an edge. In the case of standard cosmological models, this "edge" is located in all directions.

Of course the singularity is nothing but the most Super Massive Black Hole there ever was.

No, the cosmological singularity is not a supermassive black hole.

 

[AlbertE]

"The Big Bang occurred at every point in space simultaneously."

How big was space when the big bang occurred?

 

[George Jones]

"The Big Bang occurred at every point in space simultaneously."

How big was space when the big bang occurred?

Observationally, we can't pin it down, but but it is theoretically possible that space has always been infinite, and current observations are consistent with both finite and infinite space.

 

[AlbertE]

This would contradict the following statement - with which I was "brought up" as it were.

"Galaxies are flying apart, this means that at one time in the past, they were all together in one place".

Is the above statement no longer true?

 

[ibysaiyan]

This would contradict the following statement - with which I was "brought up" as it were.

"Galaxies are flying apart, this means that at one time in the past, they were all together in one place".

Is the above statement no longer true?

Check this out...
http://www.astro.ucla.edu/~wright/BBhistory.html

 

[marcus]

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

Albert if you want to gradually get to understand standard expansion cosmology I susect you first need to get rid of the highlighted idea. I don't want to say it's WRONG (today's models are not final and can always be revised, they are just the most reliable accurate picture we've been able to construct so far) but it is a misconception from the standpoint of modern cosmology. It has nothing to do with the way working cosmologists think.

Current models they use to fit observational data to are not that of an explosion outward from some point in empty space.

... which of my options would it most look like at this point in time - today - if I were able to hold all the matter in my hand in the shape it had come to form.

Since matter is not supposed to be traveling outwards into empty space, away from some central point, there would not be any "overall edge shape" that it had "come to form".

So you are asking about something that is simply not part of our conception of the universe.
The question is based on a false premise and does not make sense.
====================

There are ANALOGIES that people use to illustrate expansion with one-dimensional or two-dimensional toy models. They can be very helpful but analogies tend to be imperfect and require care.

One analogy is a CIRCULAR RING with no surrounding space. All existence concentrated in this infinitely thin ring. Galaxies and stars are one-dimensional, little dots and dashes specklend along this ring.

As the ring expands it describes a flaring cone-shape, or a bell shape. The ring represents SPACE and the bell which it describes as it expands is SPACETIME, in this toy analog picture.

that particular analogy doesn't appeal to me personally, but you see picturesque versions of it around and about. Some NASA outreach documents use it as a kind of impressionistic illustration.

Another analogy is where today's space and the galaxies in it are infinitely thin two-dimensional, like all existence (all space all matter) concentrated in the surface of a spherical balloon.

In cosmology we do not assume there is any "space around space" or any "boundary" or border to space, or any "central point" from which things spread out. Therefore to get the good from this analogy we must imagine no inside or outside of the balloon. There is no surrounding 3D space, and therefore of course no center. Only the pure infinitely thin surface of the balloon exists. The mental concentration involved in thinking the balloon analogy can take some time to get used to.
=============

Those are just lower dimensional ("infinitely thin") analogies, that may or may not help you.
The goal is to be able to think of edgeless boundaryless THREE-dimensional space, with no "space outside of space"---i.e. all existence concentrated in this full-bodied 3D space that we experience.

And no center from which it is expanding. And since there is no "outside" it can have no shape as seen from the outside. No person looking from the outside, or "holding it in my hand" as you said.

We experience the expansion and the curvature of this 3D space INTERNALLY, by witnessing large triangles that do not add up to 180 degrees (as they would in a zero curvature space).
We do not stand outside to view the curvature, it is something experienced by creatures within the space. Likewise expansion. We witness it in several ways, not only in the enlargement of wavelengths of light and the cooling of background temperature but also in the curious fact that beyond a certain distance objects actually look LARGER (take up wider angle in the sky) the farther away.

this strange beautiful optical effect of expansion is something to understand. It is as if the ancient sky was smaller and so objects of a given size (e.g. compression waves in a cloud of gas) took up a wider sector of the sky. and so they look bigger than more recent objects the same size would look.

I'm telling you to think of "shape" that is geometry as something experienced from the inside, from within the space that realizes that geometry, that curvature, that expansion.
Geometry and the change it undergoes are not something to visualize from the outside, because there is no outside.

(according to the normal cosmic model that folks use, and fit their observational data to.)

(of course as I think you know there are those more speculative models in which there is a higher-dimensional outside surrounding our space but they aren't needed to fit data to and aren't used in normal everyday cosmology.)

 

[marcus]

This would contradict the following statement - with which I was "brought up" as it were.

"Galaxies are flying apart, this means that at one time in the past, they were all together in one place".

Is the above statement no longer true?

That never was the idea. "flying apart" is a kind of poetical half-truth.
"one place" is a highly misleading expression since it suggests a point sitting in empty space.
That was certainly never the idea even if you go back to the beginnings of expansion cosmology in the 1920s.

Those words are more appropriate to irresponsible JOURNALISM than to an honest description of the usual expansion model cosmos.

 

[AlbertE]

"The goal is to be able to think of edgeless boundaryless THREE-dimensional space, with no "space outside of space"---i.e. all existence concentrated in this full-bodied 3D space that we experience."

I need pictures. :(

 

[AlbertE]

I need pictures - DEFINATELY :)

 

[ibysaiyan]

I need pictures - DEFINATELY :)

Not to sound rude but why are you so keen into visualizing things , I agree Einstein's mind worked that way however , he did extensive study . Marcus has given you an excellent detail even beyond what your typical first year UG books cover.

 

[marcus]

...Marcus has given you an excellent detail even beyond what your typical first year UG books cover.

Thanks for the positive evaluation, Ibysaiyan! A good comment like that now and then makes the effort to write about cosmology worthwhile.

 

[Naty1]

Lets suppose for a moment the big bang DID begin at some point in space...like from a stick of dynamite...a discussion by Alan Guth [originator of Inflation Theory, this from THE INFLATIONARY UNIVERSE], 1997]:

..light is emitted and matter strewn outward. After a short time light would have moved beyond the matter we ride on...the light [radiation] would disappear, so why can we see it [all around us]??

He is referring here to that fact the cosmic micowave background radiation [CMBR]is all around us and very uniform in all directions.

he goes on to explain: ..The Friedman Robertson walker [FRW] cosmological model [which closely matches our astronomical observations] was constructed to be homogeneous and isotropic.

...This means matter is assumed to have uniformly filled all of space at all times, right back to the instant of the big bang. There is no edge and no center to the distribution of matter. Since matter fills all of space, it is impossible for the radiation to leave the matter filled region as it would for a stick of dynamite.

Why believe this model?

...because a localized explosion cannot explain the observed uniformity in the CMBR. Either we would have to be at the exact spot the explosion happened or else we would observe a local hotspot

from the heavens around us. And the extreme uniformity of the CMBR, about 1 part in 1000,000 variation, means the background was extremely uniform as modeled, and is a virtually perfect black body emitter as expected. Things must have been very uncomplicated, very uniform, when this ancient radiation was emitted...

 

[marcus]

"The goal is to be able to think of edgeless boundaryless THREE-dimensional space, with no "space outside of space"---i.e. all existence concentrated in this full-bodied 3D space that we experience."

I need pictures. :(

Yes you need pictures, we all use mental diagrams, sketches, which illustrate useful analogies. But you also need PATIENCE. Feed your brain honest concepts little by little and give yourself time for it to soak in.

The balloon model of expanding geometry is only a toy analog (in reduced dimensionality, no thickness) but it might be good for you to watch the actual movie.
Google "wright balloon model".
It is different each time so watch several times.
Notice that each galaxy stays in the same place on the balloon, while the photons of light move from place to place always traveling the same speed.

On my computer screen it looks as if the speed of light is constant at about one centimeter per second, or about 1/3 of an inch per second.

You will see distances between pairs of stationary galaxies increasing faster than that, if they are far enough apart (larger distances increase more rapidly).

I keep the link to "wright balloon model" in my signature at the end of the post, for easy access. It can help a lot, even though it is only a 2D infinitely thin analogy. Pictures help. Repeated exposure helps. Give yourself time for ideas to sink in.

 

[Ken G]

We experience the expansion and the curvature of this 3D space INTERNALLY, by witnessing large triangles that do not add up to 180 degrees (as they would in a zero curvature space).

Be careful, that is actually a misconception that the balloon analogy tends to confer (that expansion of space is somehow connected with curvature of the space), because a balloon has spatial curvature but the current Big Bang model does not. People used to wonder if the universe curved back on itself like a balloon, and if it did, then we'd have this nice 2D version of the 3D universe we can use in analogies. But when such curvature was looked for and not seen, and indeed we instead found good reason to expect the universe to be spatially flat (due to inflation, perhaps), somehow the balloon analogy did not get put in the dustbin where it belongs! The universe does not need to be spatially curved in order to be able to expand, so triangles can add up to 180 degrees and still have all the effects that you mention. Indeed, that is exactly the state of affairs in the current best models.

What's more, expansion of a balloon (and expansion during inflation) tends to reduce spatial curvature with time, but general relativity (with no cosmological constant term) causes spatial curvature to grow with time-- that's kind of hard to do with balloons because balloons don't use curved time! Note that Ned Wright acknowledges this weakness in the model you cite when he says "Since this analogy uses a spherical spatial section, it corresponds to a closed Universe which recollapses." That is not the current expectation in modern cosmology, as he well knows. But analogies are always a mixed bag.

Despite its flaws, I think a better analogy is the "raisin bread rising in the oven" analogy-- it is both spatially 3D, and has no spatial curvature, yet allows raisins (galaxy clusters) to get farther apart with time. Like you say, it is still just an analogy-- and unfortunately still has the problem of seeming to require a boundary and an "external space". But this is an infinitely large loaf of raisin bread, so it's better for understanding the effects of expansion than it is for understanding why we don't need any boundaries, or any "external space", in the model. The balloon analogy is better for seeing why there doesn't have to be any boundaries, but comes at the expense of being not at all the current way we visualize the expansion, so it may be too high a price to pay! Resolving one misconception at the price of a bunch of new ones, and so forth.

Although it is highly unorthodox, I prefer to just imagine (as a working picture, the observations do not adjudicate the point and nature is probably ambivalent) that matter and rulers are shrinking, and this resolves all the misconceptions, but comes at a price of requiring us to think very differently about what distance is!

 

[marcus]

Be careful, that is actually a misconception that the balloon analogy tends to confer (that expansion of space is somehow connected with curvature of the space), because a balloon has spatial curvature but the current Big Bang model does not. People used to wonder if the universe curved back on itself like a balloon, and if it did, then we'd have this nice 2D version of the 3D universe we can use in analogies. But when such curvature was looked for and not seen, and indeed we instead found good reason to expect the universe to be spatially flat (due to inflation, perhaps), somehow the balloon analogy did not get put in the dustbin where it belongs! The universe does not need to be spatially curved in order to be able to expand, so triangles can add up to 180 degrees and still have all the effects that you mention. Indeed, that is exactly the state of affairs in the current best models.
...

No analogy is perfect. Raisinbread illustrates some things. Balloon illustrates some things (like some distances growing faster than the photons move, like galaxies staying at the same place on the balloon, analogous to being at rest relative to CMB).

In fact we do witness large triangles that do not add up to 180 degrees. Space is obviously not perfectly flat. Curvature was looked for and was seen in 1919 by Sir Arthur Eddington's group. And countless times since then by other observers.

I do not say anything about the OVERALL average curvature. Space could have overall zero curvature. We actually do not know. So I am an agnostic about that. You seem convinced with a high degree of certainty

BTW I did not say (as you seem to think I did) that space has to be curved in order to expand. The infinite raisin bread analogy, if you can picture raisin bread with no boundary, illustrates that uncurved expansion very well. I think you are over-interpreting the balloon analogy if you think it means curvature is required for expansion. It doesn't say that, nor did I. It can be useful to have several analog models. Raisin bread is good too

 

[Ken G]

In fact we do witness large triangles that do not add up to 180 degrees. Space is obviously not perfectly flat. Curvature was looked for and was seen in 1919 by Sir Arthur Eddington's group.

But not on cosmological scales. It is cosmological space that is what we say is expanding, and has never been observed to be anything but flat. So the current best Big Bang model involves a completely flat space on the scales of the cosmological principle. Hence, there is no need to connect expansion, which is something that happens at the largest scales, with triangles that add up to less than 180 degrees (as on balloons), which is not something that happens at the largest scales (so far as we know).

I do not say anything about the OVERALL average curvature. It could have overall zero curvature. We actually do not know. So I am an agnostic about that. You seem convinced with a high degree of certainty

Actually, I say nothing about what the universe is actually doing, we can only see so much of it anyway. I'm talking about what evidence we actually have to go on, and how we incorporate that evidence into our current best model-- which is flat, not like a balloon. Therefore, we don't want people to think that for space to expand and have no boundaries in our model, then our model must curve like a balloon-- what is really used is simply an infinite model, that is flat.

 

[Ken G]

This all might seem like a fairly moot issue, but in fact it has a lot to do with how we teach cosmology. The possibility of global curvature is almost always included as a central part of the cosmological possibilities, and then the balloon analogy is used with the case of a closed universe, as Ned Wright does. 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. So much wasted overhead goes into getting students to understand the possibility of spatial curvature, and then we just turn around and throw all that overhead away when we get to the actual observations and the current best models-- which are both flat! The flatness of space on cosmological scales is about as important of a cosmological principle as there is.

 

[marcus]

...
Although it is highly unorthodox, I prefer to just imagine (as a working picture, the observations do not adjudicate the point and nature is probably ambivalent) that matter and rulers are shrinking, and this resolves all the misconceptions, but comes at a price of requiring us to think very differently about what distance is!

... 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. So much wasted overhead goes into getting students to understand the possibility of spatial curvature, and then we just turn around and throw all that overhead away when we get to the actual observations and the current best models-- which are both flat! The flatness of space on cosmological scales is about as important of a cosmological principle as there is.

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. 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.

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.

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.

 

[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.