Is the Universe Finite, or Is It Infinite?

[Greg Bernhardt]

Standard cosmological models come in three flavors, open, flat, and closed,[Carroll] whose spatial curvatures are negative, zero, and positive. The open and flat types have infinite spatial volume. The closed one has finite spatial volume; spatially, it is the three-dimensional analog of the surface of a sphere. Since all three are solutions to the Einstein field equations, the finiteness or infiniteness of the universe is something that cannot be determined solely by logic but only by observation.
Current observations of the cosmic microwave background’s anisotropy show that our universe is very nearly flat.[Komatsu] If it is exactly flat, then it is a special case lying on the boundary between the more general open and closed cases. However, the range of uncertainty in the curvature is wide enough to be consistent with either positive or negative curvature, so right now...

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[phinds]

I would add to your correct statements the observation that since the universe is flat to within our ability to measure it, and that it COULD be any flatness at all, it's one hell of a co-incidence if it, out of all the infinite possible values, just HAPPENS to be very very close to flat. That's no proof of anything, of course, just an observation.

 

[PeterDonis]

it's one hell of a co-incidence if it, out of all the infinite possible values, just HAPPENS to be very very close to flat

Whether or not it is a coincidence depends on the underlying model you are using. In inflation models, this is not a coincidence since the dynamics of inflation models drive the universe towards flatness regardless of its initial spatial curvature.

 

[phinds]

Whether or not it is a coincidence depends on the underlying model you are using. In inflation models, this is not a coincidence since the dynamics of inflation models drive the universe towards flatness regardless of its initial spatial curvature.

I understand but is it not possible, at least, to have an initial condition that even inflation would not drive to near flatness?

 

[PeterDonis]

is it not possible, at least, to have an initial condition that even inflation would not drive to near flatness?

It's not just a question of the initial condition but of the inflaton field strength and the time inflation lasts. All of those are adjustable parameters in the inflation model. Mathematically, it is of course possible to find combinations of such parameters that will not result in near flatness at the end of inflation, but the range of combinations that will result in near flatness is quite large enough to make it not a "coincidence" that an inflation model predicts near flatness for our universe.

 

[phinds]

Thanks.

 

[timmdeeg]

We have been discussing this question already quite often. The details around inflation theories aren’t helpful because euclidean flatness requires that the universe had this property already before inflation. It seems very doubtful that observation can ever solve the question whether or not the universe is spatially infinite.

 

[PeroK]

It seems very doubtful that observation can ever solve the question whether or not the universe is spatially infinite.

Observations could prove the universe is finite. If it is infinite, then that may be unprovable experimentally.

 

[PeterDonis]

If it is infinite, then that may be unprovable experimentally.

If we observed that the universe's spatial curvature was negative, with flatness (zero spatial curvature) no longer within error bars, I think that would show that the universe was spatially infinite. The issue with our current observations is that positive, zero, and negative curvature are all within the error bars.

 

[PeroK]

You would still be dependent on the theory that it must, therefore, be infinite. The observation of negative curvature is not a completely watertight proof.

 

[PeterDonis]

You would still be dependent on the theory that it must, therefore, be infinite. The observation of negative curvature is not a completely watertight proof.

Neither is the observation of positive curvature by this logic, since we would also be dependent on theory to tell us that the universe must be finite in this case.

 

[PeroK]

Neither is the observation of positive curvature by this logic, since we would also be dependent on theory to tell us that the universe must be finite in this case.

A finite measurement might be definitive. Like the measurement of the size of the Earth. You may never have the same degree of certainty that something is infinite.

 

[PeterDonis]

A finite measurement might be definitive. Like the measurement of the size of the Earth.

The only way to measure the finite size of the Earth directly (i.e., without using information from outside the Earth itself, which cannot be done for the universe) is to actually circumnavigate it. We are certainly not talking about that kind of measurement in this thread; we are talking about a definite observation of positive curvature for the portion of the universe we can see. That's not the same thing. Just measuring that a portion of the Earth you can see has positive curvature doesn't tell you that the Earth as a whole is finite; you would need to rely on some kind of theory for that.

 

[timmdeeg]

In other words for Eratosthenes to assume positive curvature was mandatory while the FLRW-Universe leaves the sign of the curvature open.

 

[PeterDonis]

for Eratosthenes to assume positive curvature was mandatory

He didn't assume positive curvature for the region he had actual observations from; those observations told him the curvature was positive in that region. The assumption he made was that that same positive curvature was constant over the entire Earth, not just the parts he had direct observations from. This is similar to the homogeneity assumption that is made in FRW models of the universe--that the spatial curvature is the same everywhere, not just where we can see. That assumption is necessary in order to infer whether the universe is finite or infinite from the observed spatial curvature in the part we can see.

 

[timmdeeg]

He didn't assume positive curvature for the region he had actual observations from; those observations told him the curvature was positive in that region.

He assumed a spherically symmetric Earth supported by earth’s shadow on the moon.

Regarding said shadow we don’t have any analogy for the universe as a whole.

 

[PeterDonis]

He assumed a spherically symmetric Earth supported by earth’s shadow on the moon.

Regarding said shadow we don’t have any analogy for the universe as a whole.

Yes, fair point; we can have external observations of the Earth's curvature, but not of the universe's.

 

[cianfa72]

Sorry, you were talking about the (global) spatial curvature of the universe. Does that actually mean assuming that every spacelike hypersurface at a given cosmological time has the same geometry ?

 

[PeterDonis]

Does that actually mean assuming that every spacelike hypersurface at a given cosmological time has the same geometry ?

The same type of geometry, but (except in the flat case), the spatial curvature varies with time because the scale factor varies with time.

 

[cianfa72]

The same type of geometry, but (except in the flat case), the spatial curvature varies with time because the scale factor varies with time.

The time you were talking of is the cosmological time I think, otherwise it doesn't make any sense to talk about it.

 

[pinball1970]

A finite measurement might be definitive. Like the measurement of the size of the Earth. You may never have the same degree of certainty that something is infinite.

A slight tangent to the conversation but still relevant to the OP. Are there measurements Webb can make that could make an infinite Universe more certain? Or certain?
On distant galaxies for instance?
Or would that be more of a situation of illuminating further galaxies but that's it?
If the universe is infinite then there will never be a telescope that can answer the question?
Thanks

 

[PeterDonis]

The time you were talking of is the cosmological time I think

Yes.

 

[PeroK]

A slight tangent to the conversation but still relevant to the OP. Are there measurements Webb can make that could make an infinite Universe more certain? Or certain?
On distant galaxies for instance?
Or would that be more of a situation of illuminating further galaxies but that's it?
If the universe is infinite then there will never be a telescope that can answer the question?
Thanks

I'm not convinced that we can use probability theory effectively in this case. There are Bayesian models that try to determine the likelihood of the various cosmological parameters, but they explicity require prior assumptions.

 

[Buzz Bloom]

My understanding may be flawed, but I think that in principle the quote in Post #7

"It seems very doubtful that observation can ever solve the question whether or not the universe is spatially infinite," timmdeeg ,​

and the quote in Post #8

"Observations could prove the universe is finite. If it is infinite, then that may be unprovable experimentally," PeroK ,​

show a divergence of opinion about the possibility of confirming the universe is finite (with positive curvature).

My understanding is that a finite positive curvature universe will at some time in the future no longer have visibility of Cosmic Background Radiation photons from the Recombination era (roughly at a universe age of 300 million years) since that era will no longer exist within the Observable universe. This concept is based on the fact that at this future time, ALL of the finite universe will be within the Observable universe, and early age periods will no longer be visible. Like Quote Reply
https://www.physicsforums.com/posts/6648344/report


Like Quote Reply
https://www.physicsforums.com/posts/6648344/report

 

[timmdeeg]

My understanding may be flawed, but I think that in principle the quote in Post #7

"It seems very doubtful that observation can ever solve the question whether or not the universe is spatially infinite," timmdeeg ,​

and the quote in Post #8

"Observations could prove the universe is finite. If it is infinite, then that may be unprovable experimentally," PeroK ,​

show a divergence of opinion about the possibility of confirming the universe is finite (with positive curvature).

My view is not sufficiently precise, I agree with @PeroK .

But what makes this discussion increasingly difficult is that under the impression of the 'Hubble Tension' its no longer so certain that we can trust the LCDM model.

 

[PeterDonis]

at this future time, ALL of the finite universe will be within the Observable universe, and early age periods will no longer be visible.

These two statements contradict each other. If the universe is finite and all of the finite universe is within the observable universe of a particular comoving observer, then photons from all eras will be visible; the ones from eras sufficiently long ago will simply have circumnavigated the universe and be coming around to you again.

That said, my understanding is that it is not the case that, for a finite universe with a positive cosmological constant, all of the finite universe will eventually be within the observable universe of a particular comoving observer. The accelerating expansion of the universe prevents this even in the finite case.

 

[Buzz Bloom]

Hi @PeterDonis:

I will try to do the math to understand the implications of your thought:

"it is not the case that, for a finite universe with a positive cosmological constant, all of the finite universe will eventually be within the observable universe of a particular comoving observer."​

This will take me quite a while since my math skills are not as easy to use as they were when I was much younger.

Regarding the interesting idea that

"photons from all eras will be visible; the ones from eras sufficiently long ago will simply have circumnavigated the universe and be coming around to you again,"​

it seems plausible that the photons from two distant time eras being at the same place in the sky would be a good clue that the the universe was finite/hyper-spherical.

Regards,
Buzz

 

[PeterDonis]

it seems plausible that the photons from two distant time eras being at the same place in the sky would be a good clue that the the universe was finite/hyper-spherical.

Yes, but that depends on it actually being possible for photons to circumnavigate the universe if it is finite. As I said, with a positive cosmological constant, my understanding is that accelerated expansion prevents this from happening: heuristically, the universe expands faster than photons can get around it.