Is the universe finite or infinite?

haruspex

[QUOTE=Ken G;3931135]The answer to that question is, "we have no scientific evidence that the universe is finite." That's it, that's all we can use science to say. /QUOTE]

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

shreyakmath

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

Ken G

It's not terribly relevant, but that doesn't follow. Space could curve back on itself, have finite volume, and still have no boundaries. But the real issue here is, despite looking very hard (and quite possibly as hard as we can ever look), we have no evidence that it does have boundaries, nor do we have any evidence that it does not have boundaries, nor do we have any evidence that it curls back on itself, nor do we have any evidence that it does not curl back on itself. All we know is, what we see looks flat, and we have no idea how long it stays looking flat. That's it, that's the scientific evidence in its entirety.
But making and testing models has nothing to do with answering the OP question. The models we make are intended as idealizations, and the standard idealization is that of a flat infinite universe. That model works quite well. Is that evidence that the universe really is flat and infinite? Of course not. If I am digging a foundation for my house, I'm certainly going to use a model that the surface of the Earth is flat and infinite (in that I will certainly not model any curvature of the Earth), and it will work great for digging my foundation, but I'm never going to conclude that any of this is evidence that the Earth really is flat and infinite.

Ken G

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

haruspex

Yes, that's the point I was making.
I'm far from expert in this area, but my understanding is that General Relativity posits a "flat" spacetime, but a finite, curved space, with a compensating curvature in time.
If so, and if you accept evidence for GR, that is surely evidence for a finite universe.
I would also have thought that an infinite universe was inconsistent with the Big Bang model, and there is much evidence for that.
You seem to be demanding much more direct evidence.
I disagree. The question was "Does it have boundaries? Is it finite?" Establishing that 'finite without boundaries' cannot be ruled out is a partial answer.

Light Bearer

lolz

Ken G

No, GR says that in comoving-frame coordinates (which is what is generally used in cosmology to talk about what the universe as a whole is doing), all the observed curvature due to gravity is in the time dimension (associated with cosmological redshifts), none is in the spatial dimension. We say the universe is "spatially flat" in this sense. The observations cannot rule out some small spatial curvature, but they can rule out the idea that the universe curves back on itself over the range that we can observe or in some way test our inferences about-- and of course we have no idea what it does beyond that range. Even if we do detect some small spatial curvature, it would not require that this curvature is maintained beyond what we can observe-- the cosmological principle applies to explanations of what we actually observe, it is not a philosophical claim about what we cannot observe.
No, the Big Bang model includes neither finiteness nor spatial curvature at present. So the model is one of an infinite universe. However, the model need not make any claims that this is actually true, it just means we have no reason to model finiteness of the universe.I said it could not be ruled out. I also said the alternative could not be ruled out. In fact there is no evidence at all either way. When there is no evidence in favor of a proposition, nor evidence against it, it doesn't leave you with a whole lot more to say, which is the point.

twofish-quant

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

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

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

Then we have dark energy and everything changed.

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

twofish-quant

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

twofish-quant

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

twofish-quant

You give up too easily.

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

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

Ken G

Right, and what we find, when we do that, is zero evidence of any spatial curvature, which is consistent with inflation. If inflation is correct, this will always be true, no matter how good our observations get.
If we detect that, you can throw away inflation completely!You don't see what I'm saying. LCDM is not a statement about what the universe is really like, it is a good model of the universe. That's a rather important distinction, and cuts right to the heart of what physics and astronomy does! What's more, LCDM is flat, and invokes the cosmological principle, and so it is a model of an infinite universe. Of course these are idealizations, physics deals exclusively in idealizations, it makes models. As I said, that does not mean it asserts the universe is infinite, it means it is an infinite model of the universe. Which is just precisely what it is. Newtonian physics was never an assertion that the universe is deterministic, it was always a deterministic model of the universe, which is quite different.

What's more, if inflation is correct, and the cosmological principle continues to be the key simplification in the Big Bang model, then this will always be true-- our model of the universe will always be flat and infinite. This is just plain fact, the logic is straightforward.
I have never been talking about "what the current model allows." The current model allows for unicorns, space aliens, and teleportation beams. But none of those are included in the current model, because there is no need for them, and no evidence in favor of them. Again this is a rather important distinction.

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

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

twofish-quant

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

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

and the WMAP for the curvature amplitude.

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

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

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

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

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

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

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

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

twofish-quant

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

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

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

Ken G

Right, but that's exactly why the CDM model was uniformly rejected by just about everyone. That is in complete contrast with the models of today, with which we often hear the phrase "precision cosmology", and has been related to several Nobel prizes.
No, that's not true. I was an astronomer in 1995 also, and few thought the universe was not flat, they thought the model was wrong. That's also why there were no Nobel prizes awarded for the CDM model. Indeed, it was considered a huge problem that the flatness parameter came out 0.3, which was way too close to 1 to not be 1 (a flatness less than 1 gets exponentially less flat with time, so to be 0.3 now, it would have had to have been extremely close to 1 in the past, but still strangely different from 1). Even in 1995, inflation was commonly taught, and it was widely expected that the flatness should be 1. The missing energy was just considered a paradox that no one knew how to solve, but made people worried that we were missing something really crucial. Today that is not the sentiment, hence all the Nobel prizes, though of course there are plenty of people still not completely happy with dark energy, and that's why we have some people claiming that you need multiverses to explain it. I'm not banking on that approach myself, however, I just think we are still missing some key physics, but the models of the universe will still be flat (except for local fluctuations with no global significance), and we will just never get to know anything beyond that for the simple reason that we cannot look.
I'm not sure where you get that, but it is incorrect. See the WMAP website at http://map.gsfc.nasa.gov/universe/uni_shape.html , where we find quotes like:
"If the density of the universe exactly equals the critical density, then the geometry of the universe is flat like a sheet of paper, and infinite in extent. The simplest version of the inflationary theory, an extension of the Big Bang theory, predicts that density of the universe is very close to the critical density, and that the geometry of the universe is flat, like a sheet of paper."
and:
"We now know that the universe is flat with only a 0.5% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe."
Which is what I have been saying.

Ken G

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

twofish-quant

Which textbooks? Graduate or undergraduate?

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

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

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