Is there any way in the future to determine the Universe's size?

davLev said:

Therefore, why don’t we consider a possibility for a flat infinite universe?

Of course, we do consider the possibility that the universe is infinite and approximately flat.

davLev said:

Therefore, why don’t we consider a possibility for a flat infinite universe?

We do! I have already said this in this thread, both before and after you joined it!

The premise under discussion is something along the lines of: given that curvature measurements hover around flatness, but have error bars that encompass all three possible cases (positive, flat, and negative curvature), what is the largest radius of curvature that can fit into those measurements and still be indistinguishable from the other cases.
That flatness is on the table is kinda built in into the topic.

As Many independent observations indicate that the universe is in fact flat (and infinite), why do we try to limit its size to 205 Gly or even 20 trillion ly?

davLev said:

As Many independent observations indicate that the universe is in fact flat (and infinite), why do we try to limit its size to 205 Gly or even 20 trillion ly?

We don't! What part of "minimum radius of curvature consistent with observation" do you not understand?

davLev said:

As Many independent observations indicate that the universe is in fact flat (and infinite), why do we try to limit its size to 205 Gly or even 20 trillion ly?

You must take into account that the probability of the universe being perfectly flat is practically zero.

Jaime Rudas said:

You must take into account that the probability of the universe being perfectly flat is practically zero.

Actually, if you treat the radius of curvature as a continuous parameter on which you have a probability distribution then the probability of any exact value is exactly zero, including the flat case. That's part of the problem here - our measurements exclude small radii, both positive and negative, but do not rule out a really large positive curvature universe, a really large negative curvature universe, or an infinite radius of curvature (i.e., a flat space), and if the universe is actually flat this will always be the case. All we will ever be able to do - at least within the bounds of relativity - is put ever larger lower bounds on exactly how vast the universe is. Only if it is actually non-flat (one way or the other) would we be able to rule out the other two cases.

A future cosmological theory, of course, may provide an answer to the question by (for example) showing that the density must be exactly equal (or unequal) to the critical density because <something>.

As there is a possibility for a flat infinite universe, does it mean that the universe age is also infinite?

davLev said:

As there is a possibility for a flat infinite universe, does it mean that the universe age is also infinite?

A flat infinite universe does not imply an infinite age in and of itself, no.

As far as I understand it some versions of inflation theory do have an infinite extent to the past, but as far as I'm aware they also imply that the universe is not flat, but they drive it to be "nearly" flat - to have a very, very, very large radius of curvature. I could be wrong - @PeterDonis would know better.

Jaime Rudas said:

You must take into account that the probability of the universe being perfectly flat is practically zero.

If it's flat, then it's flat; and probability theory doesn't come into the equation.

In the article it is stated:
“Many independent observations indicate that the universe is in fact flat”
So why do we refuse to accept the fact that the universe is just flat?
Why do we insist to push the idea of nearly flat & curvature to our flat universe?
Is it just because there is no valid theory for that infinite flat universe?

davLev said:

In the article it is stated:
“Many independent observations indicate that the universe is in fact flat”
So why do we refuse to accept the fact that the universe is just flat?
Why do we insist to push the idea of nearly flat & curvature to our flat universe?
Is it just because there is no valid theory for that infinite flat universe?

"Flat" means the spatial curvature of the universe is exactly zero. But we can never observe any continuous physical parameter to be exactly some value. There are always error bars in our measurements. The OP of this thread was basically asking how wide the error bars are.

Please bear in mind that this is not your thread and the fact that you personally don't appear to care about a particular question does not mean other people don't care about it or that discussion of it is not worthwhile. If you have nothing substantive to add to the discussion, please do not post.

davLev said:

In the article it is stated:
“Many independent observations indicate that the universe is in fact flat”

The key word is indicate. This means suggest rather than prove.

davLev said:

So why do we refuse to accept the fact that the universe is just flat?

No one refuses to accept it. It's simply unproven.

davLev said:

Why do we insist to push the idea of nearly flat & curvature to our flat universe?

Because all experiments have a margin of error. The experiments so far can only show flatness to within the relevant experimental error.

davLev said:

Is it just because there is no valid theory for that infinite flat universe?

Precise flatness may be a theoretical issue, but that's not the main issue, which is allowing for experimental error.

Speaking for myself, the honest answer is that we don't know.

davLev said:

Is it just because there is no valid theory for that infinite flat universe?

No. Our current theory covers the possibility of a flat universe just fine.

PeroK said:

If it's flat, then it's flat; and probability theory doesn't come into the equation.

For the universe to be perfectly flat, it would need to be perfectly homogeneous, and it is not.

Jaime Rudas said:

For the universe to be perfectly flat, it would need to be perfectly homogeneous

All of the observations described in this thread are of the average spatial curvature of the universe. Obviously its spatial curvature cannot be the same everywhere since the matter and energy in it is clumped.

davLev said:

“Many independent observations indicate that the universe is in fact flat”

I suspect Siegel is over-reaching here, as well as what has been said above. I think the correct statement is that many independent observations are consistent with flatness and none are significantly inconsistent with it, but all are also consistent with a very large radius of curvature.

PeterDonis said:

All of the observations described in this thread are of the average spatial curvature of the universe.

I agree. That's why I mentioned that the probability of the universe being perfectly flat is practically zero.

Jaime Rudas said:

That's why I mentioned that the probability of the universe being perfectly flat is practically zero.

We are not talking about the probability of the entire universe being perfectly spatially flat. We are talking about the probability of the average curvature of the universe being zero, i.e., flat. That's not the same thing.

Also, since a universe which is on average positively curved is spatially closed, it has a different spatial topology from either the flat or open cases, so it is not just a question of a continuous variation in the curvature parameter; there is discontinuous choice of spatial topology involved. So just looking at things from the standpoint of a continuous probability measure is not correct.

davLev said:

Why do we insist to push the idea of nearly flat & curvature to our flat universe?
Is it just because there is no valid theory for that infinite flat universe?

A model of a flat universe works just fine with current theory (general relativity is the underlying theory).
A model of a curved universe works just fine with current theory.
A model with a 'center' or with 'edges' does not work fine with current theory.

You confirm that there is a possibility for the universe to be infinite flat.
You also confirm that the current theory can cover this infinite flat universe.
Do we have any real observation that clearly proves that the universe has a curvature?
As we consider a possibility for positive and negative curvature, why can’t we also consider one more possibility for the universe to be an infinite flat without any curvature?

davLev said:

You confirm that there is a possibility for the universe to be infinite flat.
You also confirm that the current theory can cover this infinite flat universe.
Do we have any real observation that clearly proves that the universe has a curvature?
As we consider a possibility for positive and negative curvature, why can’t we also consider one more possibility for the universe to be an infinite flat without any curvature?

Your questions have already been answered. Since you apparently have nothing further of substance to contribute, you have now been banned from further posting in this thread.

davLev said:

why can’t we also consider one more possibility for the universe to be an infinite flat without any curvature?

There's either an echo or a closed timelike curve in here...

Please stop repeating yourself, Ibix.