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

[Cerenkov]

Thank you for this excellent explanation, Bandersnatch.

You’ve covered all of the points that were of interest to me in a way that helps me understand them much better.

So, I thank you for your efforts and I also extend my thanks to Jaime Rudas, Peter Donis, Ibix and Hornbein for their helpful input in this thread.
Cerenkov.

 

[davLev]

Yes, it's true: when omega k is -0.005 we have a positively curved universe of radius 205 Gly and when omega k is +0.007 we have a negatively curved universe of radius 173 Gly

Do you mean that the minimal universe radius around us is 173Gly while the maximal radius is 205Gly?
That means that we are located at the centre of the universe.
However, what is the chance that we are so lucky to be exactly at that centre?
Just a brief calculation:
Lets assume that the radius of the universe is 5R
The total volume is reference to 125R^3
The total volume for the segments 1 -4 is
Reference to 64 R^3
While the volume foe the first segment is 1R^3
Therefore, the chance to be at the center (first segment)is 1 to 125
The chance to be st anywhere from 1-4 is
64 to 125 (about 51 %)
The chance to be at the last 5th segment is 61 to 125 (about 49%)
Therefore, our statistical chance to be close to the edge of the universe is very high.
So how can you claim that tbe maximal universe size is only 205 ly?

 

[Ibix]

Do you mean that the minimal universe radius around us is 173Gly while the maximal radius is 205Gly?

No - these are radii of curvature of the hypersphere (in the positive case) or hyper-hyperboloid in the negative case. Neither is a distance in any direction unless you embed your universe in a higher-dimensional space (fine in a model, but there's no evidence for higher dimensions in reality) and measure in that.

That means that we are located at the centre of the universe.

There is no center or edge in any of these models. In the negative curvature case the universe is infinite. In the positive curvature case it is a three-sphere with a circumference $2\pi$ times the quoted radius. If you travel that far (which may not be possible in the lifetime of the universe) you would return to your start point, just like circumnavigating a two-sphere like the surface of the Earth.

 

[Jaime Rudas]

Do you mean that the minimal universe radius around us is 173Gly while the maximal radius is 205Gly?
That means that we are located at the centre of the universe.

No, according to our estimations, the universe doesn't have a center. This means that the universe can be finite or infinite, but in both cases, it would be unbounded. Since it has no boundaries, it cannot have a center.

Imagine that the universe is the surface of a sphere (only the surface, not its interior); under those conditions, no point on that surface (universe) would be its center, and in fact, the center would not exist.

It is important to note that the surface of a sphere has two dimensions, while if the universe is finite, we consider it as the surface of a three-dimensional sphere, known as a 3-sphere.

 

[davLev]

In the following article:
https://www2.lbl.gov/Science-Articles/Archive/SNAP-3.html
It is stated:
“Many independent observations indicate that the universe is in fact flat”
Therefore, why don’t we consider a possibility for a flat infinite universe?
If we go to the left 100 trillion ly we would stay at the left.
Just an infinite universe without any curvature.

 

[Jaime Rudas]

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.

 

[Ibix]

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!

 

[Bandersnatch]

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.

 

[davLev]

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?

 

[Ibix]

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?

 

[Jaime Rudas]

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.

 

[Ibix]

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>.

 

[davLev]

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

 

[Ibix]

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.

 

[PeroK]

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.

 

[davLev]

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?

 

[PeterDonis]

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.

 

[PeroK]

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.

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.

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.

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.

 

[PeterDonis]

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.

 

[Jaime Rudas]

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.

 

[PeterDonis]

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.

 

[Ibix]

“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.

 

[Jaime Rudas]

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.

 

[PeterDonis]

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.

 

[Drakkith]

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.

 

[davLev]

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?

 

[PeterDonis]

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.

 

[Ibix]

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...

 

[Cerenkov]

Please stop repeating yourself, Ibix.