Does flat spacetime geometry prove the universe is infinite?

[Ehyeh Asher Ehyeh]

TL;DR

No answer could be more important to the assumptions and approach to cosmology. The overwhelming bias is a finite Universe, and could this be a mistake?

Summary: No answer could be more important to the assumptions and approach to cosmology. The overwhelming bias is a finite Universe, and could this be a mistake?

The measurements across the observable universe strongly indicate a Gaussian Curvature of Zero(Flat).
Does this prove that Spacetime is infinite and that the Universe itself is infinite and eternal?

 

[Ibix]

No.

Our model that best matches our observations is a spatially flat universe that is infinite in extent. I believe it includes a start at a finite time in the past, although I am not completely certain I'm up to date with that claim.

But none of this proves anything. Our model could be wrong in some subtle way we haven't spotted yet. In fact, we're almost certain that general relativity is only an approximation to a quantum theory of gravity. Developing a working theory of quantum gravity might change our conclusions radically.

This thread might be better in Cosmology - I'll recommend it be moved.

 

[Ehyeh Asher Ehyeh]

Ibix,
They talk about Inflation and the rapid expansion of Spacetime at the Big Bang, but what is really meant by this? Space expanded into itself?
Or does it mean that Negative Curvature Spacetime with a corresponding low energy/mass was upgraded to a Flatter Spacetime with higher energy and less Negative Curvature?

 

[Ibix]

what is really meant by this?

Roughly speaking, it means that the distance between observers who see the CMB as isotropic grows over time. "Space is expanding" is a rather inaccurate way that people try to put it.

 

[Ehyeh Asher Ehyeh]

Roughly speaking, it means that the distance between observers who see the CMB as isotropic grows over time. "Space is expanding" is a rather inaccurate way that people try to put it.

"The simplest cosmology that fits the large-scale characteristics of the universe is the so-called Friedmann—Lemaître—Robertson—Walker cosmology describing a spacetime that is homogeneous (same everywhere) and isotropic (has no preferred direction).This simple cosmology is characterized, among other things, by a variable that represents spatial curvature. It can be positive, negative, or zero.
Our best observations to date strongly suggest that the universe has no spatial curvature. It may be expanding in time, but the geometry of space, at any given time, is Euclidean.
The simplest topology that corresponds to Euclidean geometry is that of flat, infinite space. So by Occam’s razor, i.e., the parsimony of assumptions, we can conclude that in the absence of evidence to the contrary, the universe appears infinite."
https://www.forbes.com/sites/quora/2018/05/23/how-do-we-know-the-universe-is-infinite/#6ca2c7207989~What I'd really be interested to know is the nature of an infinite Spacetime of negative Gausian Curvature; 1. Would the curvature become infinite and therefore unstable? 2. And at what subset of infinity would this instability occur if it exists? 3. What quantity of Negative Curvature Spacetime would be required to equal the mass/energy of the Observable Universe?
~An entirely new approach might also be to assume that the current accelerating expansion is not the result of internal compressive forces but of external tension achieved by the Positive Curvature material of this Universe being pulled by a surrounding encapsulation by Negative Curvature Spacetime. In essence our Universe is being pulled apart by a Spacetime Gradient more or less equivalent to falling down a mountain.
~And lastly, the Zero Net Energy Universe hypothesis is supported by a Zero Curvature Universe Spacetime. So when lumpy positive curvature material exists it's also an extension of negative curvature Spacetime that is required to produce a flat average overall.

 

[PeterDonis]

What I'd really be interested to know is the nature of an infinite Spacetime of negative Gausian Curvature; 1. Would the curvature become infinite and therefore unstable?

No. A spacetime with negatively curved spacelike hypersurfaces does not need to have infinite spatial curvature.

What quantity of Negative Curvature Spacetime would be required to equal the mass/energy of the Observable Universe?

The question doesn't make sense; "negative curvature spacetime" doesn't have a mass/energy.

An entirely new approach might also be to assume that the current accelerating expansion is not the result of internal compressive forces but of external tension achieved by the Positive Curvature material of this Universe being pulled by a surrounding encapsulation by Negative Curvature Spacetime. In essence our Universe is being pulled apart by a Spacetime Gradient more or less equivalent to falling down a mountain.

Where are you getting this from?

 

[Ehyeh Asher Ehyeh]

I'm not so sure. The Singularities often discussed have Infinite positive Curvature, and I'm not sure that there isn't the inverse equivalent.
All Spacetime has mass/energy and time incorporated into the fabric. It is a small amount for flat Spacetime, a large amount for positive curvature Spacetime and likely a much smaller amount for negative curvature Spacetime.
And it is being discussed that the Vaccuum that may be encapsulating this Universe is the force responsible for the accelerating expansion and may in fact be the cause of the Big Bang. But of course these Cosmologists are in the minority who accept that the Universe may indeed be infinite and eternal.
~ If the required forces are not internal, then they are external?

 

[PeterDonis]

All Spacetime has mass/energy and time incorporated into the fabric. It is a small amount for flat Spacetime, a large amount for positive curvature Spacetime and likely a much smaller amount for negative curvature Spacetime.

This is nonsense. Where are you getting this from?

it is being discussed that the Vaccuum that may be encapsulating this Universe is the force responsible for the accelerating expansion and may in fact be the cause of the Big Bang. But of course these Cosmologists are in the minority who accept that the Universe may indeed be infinite and eternal.

Who is discussing this? Please give a reference.

 

[Ehyeh Asher Ehyeh]

This is nonsense. Where are you getting this from?
Who is discussing this? Please give a reference.

"We can measure the energy density of the vacuum through astronomical observations that determine the curvature of spacetime. All the measurements that have been done agree that the energy density is VERY CLOSE TO ZERO. In terms of mass density, its absolute value is less than 10-26 kilograms per cubic meter."~http://math.ucr.edu/home/baez/vacuum.html
~The Quantum Field has particles, virtual particles, electromagnetic energy and time built into it. Negative curvature Spacetime then is rarefied to yield a lower energy density than flat Spacetime as you might expect. Matter is just an extension of Spacetime after all.
~And so you have no problem that a Singularity of Infinite Spacetime like a black hole can gobble up Spacetime, but there is nothing at work spitting it out?

 

[PeterDonis]

We can measure the energy density of the vacuum ...

None of the things in that article have anything to do with what you were saying.

The Quantum Field has particles, virtual particles, electromagnetic energy and time built into it. Negative curvature Spacetime then is rarefied to yield a lower energy density than flat Spacetime as you might expect. Matter is just an extension of Spacetime after all.

This is nonsense. Thread closed.