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

[Maximum7]

TL;DR

Trying to think of speculative ways to measure the size of the universe (if measurable)

I am frequently contemplating the size of the universe. Logic tells me that existence cannot is end as there really can’t be anything as anti-existence but if the universe loops back on itself; it may not be an issue. Is there a possible way in the far future to semi-accurately measure its size? I know the Cosmological Event Horizon may prevent this but could we also confirm accurately that it is infinite and immeasurable? I know we have recently been trying to detect gravity waves; but I don’t know if that can do it. My futurist friend doesn’t know either

 

[Ibix]

You can estimate the size by looking at the scale of fluctuations in the cosmic microwave background. How they look depends on the overall curvature of the universe.

Our current best measure is that it is indistinguishable from a flat infinite universe.

 

[davLev]

Why is it so difficult for the science community to admit that the universe is infinite or almost infinite?

 

[PeterDonis]

Why is it so difficult for the science community to admit that the universe is infinite or almost infinite?

Why do you think the scientific community has any such difficulty?

 

[phinds]

Why is it so difficult for the science community to admit that the universe is infinite or almost infinite?

There is no such thing as "almost infinite". It's either infinite or finite. There is no definitive evidence as to which it is.

 

[berkeman]

There is no such thing as "almost infinite".

$\infty - skosh$

 

[Ibix]

Why is it so difficult for the science community to admit that the universe is infinite or almost infinite?

"It's infinite, or so huge that we can't see any curvature" is what I said in the post right above yours. Did that seem like a difficult admission?

 

[Vanadium 50]

"Almost infinity" is like "pretty unique".

 

[timmdeeg]

Why is it so difficult for the science community to admit that the universe is infinite or almost infinite?

For the universe to be infinite requires spatial flatness in the sense of mathematically euclidean flatness. There is no way to prove that however by observation. The tiniest deviation from euclidean flatness could e.g. still mean that we live in a very very large sphere.

 

[davLev]

Is there a possibility to specify the minimal size for that “very very large universe sphere”?
I assume that it should be above the 92bly observable universe size.
Could it be above one trillion ly?

 

[Hornbein]

For the universe to be infinite requires spatial flatness in the sense of mathematically euclidean flatness. There is no way to prove that however by observation. The tiniest deviation from euclidean flatness could e.g. still mean that we live in a very very large sphere.

A hyperbolic Universe would be infinite and not flat.

 

[Hornbein]

Is there a possibility to specify the minimal size for that “very very large universe sphere”?
I assume that it should be above the 92bly observable universe size.
Could it be above one trillion ly?

We can say with 99.87% confidence that the radius is at least 170 gigalightyears.

According to Stack Exchange the visible Universe has a radius of 46 Gly.

 

[davLev]

Thanks

 

[Cerenkov]

We can say with 99.87% confidence that the radius is at least 170 gigalightyears.

According to Stack Exchange the visible Universe has a radius of 46 Gly.

Hello Hornbein. Could you please say how the level of confidence and the radius were derived?

Are they the result of your own calculations?

Or is there a source that you could direct me to please?

Many thanks for any help given.Cerenkov.

 

[timmdeeg]

A hyperbolic Universe would be infinite and not flat.

Therefor I mentioned the Sphere as an example.

 

[Hornbein]

Hello Hornbein. Could you please say how the level of confidence and the radius were derived?

Are they the result of your own calculations?

Or is there a source that you could direct me to please?

Many thanks for any help given.Cerenkov.

https://www.physicsforums.com/threads/the-curvature-and-size-of-the-universe.1050389/

 

[Bandersnatch]

We can say with 99.87% confidence that the radius is at least 170 gigalightyears.

According to Stack Exchange the visible Universe has a radius of 46 Gly.

As was pointed out in the thread you referenced, the Omega_k value to use should be 0.001 - 3×0.002 = 0.005. There needs to be a minus there, otherwise you're calculating the radius of curvature of a hyperbolic universe. So the correct value for the radius is ~205 Gly.

Furthermore, as was also discussed, this is the radius of curvature. It is not directly comparable with the size of the observable universe. To do that, you need the circumference of the corresponding hypersphere, which comes out to approx. 1288 Gly.

 

[Cerenkov]

My thanks to Hornbein and Bandersnatch.However, if I could ask for some clarification that would be very helpful.

I understand the radius of a simple sphere to be 1/2 its diameter. Therefore I take the diameter of the observable universe to be 2 x 46 Gly, yielding a total of 92 Gly.

But when it comes to a hypersphere and the radius of the curvature of said hypersphere, I'm afraid I'm going to need a little help.

I do understand that travelling within a hypersphere means never coming to its boundary or edge, making it different from a simple sphere, where its possible to leave the centre and arrive at the boundary.

But could you please explain what is meant by 'the radius of curvature of a hypersphere' in a way that I'm likely to comprehend, given my Basic level of membership?

Thanks again for your help and for any further help given.Cerenkov.

 

[Hornbein]

The radius and diameter and circumference work the same way no matter how many dimensions you may have. (I've found this quite useful in the weird things I like to do.)

 

[Ibix]

When we talk about a spherical universe we are talking about a space analogous to the surface of the Earth, not its interior (topologists would call the Earth a ball - it is only its surface that is called a sphere). The surface of the Earth can be used as a lower-dimensional analogy to a spatial slice of a closed universe. You can travel in any direction endlessly, and can end up where you started by travelling in what looks, locally, like a straight line. In this analogy, the observable universe is the interior of a circle drawn around your current position. If the circle is large enough you can see that the circumference isn't quite $\pi$ times the distance across it due to the curvature, but we can't see that in reality, which is one way to put a lower bound on the minimum curvature of the universe as a whole.

 

[Bandersnatch]

The 3d space we live in is on the surface of the hypersphere. Its radius is in the fourth spatial dimension.
The size of our universe is analogous to the size of a circle drawn on the surface of a 2d sphere.
In both cases the radii of the sphere (curvature) are not something existing on the surface.

 

[Cerenkov]

My thanks to Hornbein, Ibix and Baluncore for their help.There's just one final matter that comes to mind.

Here is my view. The standard deviation of the measurement is 0.002. Let's use three standard deviations to get magnitudes of 0.001 + 3*0.002 = 0.007. I then can say with 99.87% confidence that the magnitude of omega is at least this high. Then the radius is at least 170 gigalightyears. We can bet safely that the radius is greater than this.

From what Hornbein wrote am I right to glean that the cited figure of a 170 Gly radius is a minimum value?

That, given what is observed and theorized, the radius of the entire universe cannot be less than this figure?Thank you,

Cerenkov.

 

[Ibix]

205Gly rather than 170, per Bandersnatch's comment, but yes that's a minimum. If it were smaller than that we ought to be able to see evidence of spatial curvature given our measurement accuracy.

 

[davLev]

Based on the following article the universe must be at least 23 trillion light years in diameter,

https://www.forbes.com/sites/starts...entire-unobservable-universe/?sh=46d47e9df806
It is stated:
Observations from the Sloan Digital Sky Survey and the Planck satellite are where we get the best data. They tell us that if the Universe does curve back in on itself and close, the part we can see is so indistinguishable from “uncurved” that it must be at least 250 times the radius of the observable part.

This means the unobservable Universe, assuming there’s no topological weirdness, must be at least 23 trillion light years in diameter, and contain a volume of space that’s over 15 million times as large as the volume we can observe.

 

[Cerenkov]

205Gly rather than 170, per Bandersnatch's comment, but yes that's a minimum. If it were smaller than that we ought to be able to see evidence of spatial curvature given our measurement accuracy.

Thank you Ibix.

Now, if you can put yourself in my (the layman's) shoes for a moment, can you see how its somewhat confusing for me to read the comments of two members who are citing estimates that differ by 35 billion light years?

While I appreciate that on the far larger scale of the entire, unobservable universe 35 Gly is small potatoes, I am puzzled by the disagreement. As a Basic level member, is it worth asking why this is or would I be diving into matters that are too far over my head?

On a different note, I think understand what you mean about the spatial curvature given the measurement accuracy. Without invoking exotic topologies, the Friedmann solutions fall into three types - closed, open and flat. So if we inhabited a universe that wasn't flat we'd see some evidence of curvature, either positive or negative. Is that right?

The Ethan Siegel article linked by davLev says...

For example, we observe that the Universe is spatially flat on the largest scales: it's neither positively nor negatively curved, to a precision of 0.25%.

So, does that mean we are 99.75 certain our universe is flat?Thank you,

Cerenkov.

 

[Cerenkov]

Based on the following article the universe must be at least 23 trillion light years in diameter,

https://www.forbes.com/sites/starts...entire-unobservable-universe/?sh=46d47e9df806
It is stated:
Observations from the Sloan Digital Sky Survey and the Planck satellite are where we get the best data. They tell us that if the Universe does curve back in on itself and close, the part we can see is so indistinguishable from “uncurved” that it must be at least 250 times the radius of the observable part.

This means the unobservable Universe, assuming there’s no topological weirdness, must be at least 23 trillion light years in diameter, and contain a volume of space that’s over 15 million times as large as the volume we can observe.

Thank you for this davlev.

Do you (or anyone else) know why there is such a great discrepancy between the figure quoted by Ethan Siegel and the ones given by Hornbein, Ibix and Baluncore?Thank you,

Cerenkov.

 

[Bandersnatch]

We talked about the Forbes article in the previous thread. You were there too. We couldn't figure out where Siegel got those numbers from. It's hard to figure out how he got there, since he doesn't provide any hints as to his method.

As for the discrepancy in our numbers, it was explained in post #17. 170 Gly is erroneous. One gets it when adding instead of deducting the error bars on the curvature measurement.

What we're doing here is dividing the Hubble radius by the square root of the (absolute value of) curvature density parameter Omega k.
The values are taken from the Planck mission's data.
The Hubble radius is just the Hubble constant expressed differently, so that's what we need.
The result will be the radius of curvature Rk.

The closer Omega k is to zero, the larger the Rk. If it is zero, then Rk is undefined (can't divide by zero) and the universe is flat. If Omega k is negative, the curvature (k) is positive, and the universe curves onto itself - like a sphere. If Omega k is positive, the curvature is negative, and the universe curves the other way - like a saddle. In the latter case it is infinite despite having a radius of curvature. The smaller the Rk, the more curved the universe. In the case of positive curvature - also smaller in overall size.

So we want to look at the values of these two, (Omega k and the Hubble constant H0) and the uncertainty in their measurement, and sort of assume the actual value lies on the most extreme end of the uncertainty. This will give us the boundaries on how curved the universe could be.

For H0, as measured by Planck, the uncertainty is tiny. Something like one percent. So we can safely ignore it for our purposes.

For Omega k, we have 0.001 +/- 0.002. That's one sigma confidence. It's like saying 'we're reasonably sure the actual value lies somewhere between -0.001 and 0.003'. If we take three times the size of the error bars, +/- 0.006, we're saying 'it's almost certain the actual value lies between -0.005 and 0.007'. So that's what we do here.

If you then take the one extreme of the value: -0.005, you get a positively curved hypersphere of radius approx. 205 Gly.
If you take the other extreme value, you get the 170 Gly, but it's now a negatively curved space.

In other words, 170 Gly is the minimum radius of curvature of a universe that curves hyperbolically, into a saddle-like shape - the other way - instead of spherically.
I.e. it's the third non-exotic possibility: the universe, is either flat, a hypersphere of Rk > 205 Gly, or is hyperbolic with Rk > 170 Gly.

If we were to use one sigma error bars, we'd get different - larger - radii, but with lower confidence.

That's all that can be said with the data Planck provided. There are further caveats:
The stated numbers represent the current-best, but still rather coarse, model and a specific set of data (the CMB, ignoring e.g. the Hubble tension) and (within this framework) with high, but not perfect, confidence. Also, more exotic possibilities are discounted (cylindrical shape? toroidal? weirdo irregular something or other?).edit: corrected the wording to represent closed universe as k>0 when Ωk<0, while the open case as k<0 when Ωk>0, as per the posts below.

 

[PeterDonis]

If you then take the one extreme of the value: -0.005, you get a negatively curved hypersphere of radius approx. 205 Gly.
If you take the other extreme value, you get the 170 Gly, but it's now a positively curved space.

In other words, 170 Gly is the minimum radius of curvature of a universe that curves hyperbolicaly, into a saddle-like shape - the other way - instead of sphericaly.
I.e. it's the third non-exotic possibility: the universe, is either flat, a hypersphere of Rk > 205 Gly, or is hyperbolic with Rk > 170 Gly.

I think you have this backwards. Negative curvature means a hyperbolic, saddle-like shape, not a hypersphere. Positive curvature means a hypersphere (3-sphere), not a hyperbolic, saddle-like shape.

 

[Jaime Rudas]

I think you have this backwards. Negative curvature means a hyperbolic, saddle-like shape, not a hypersphere. Positive curvature means a hypersphere (3-sphere), not a hyperbolic, saddle-like shape.

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

 

[Bandersnatch]

Yes, you're right, both of you. I was thinking of the sign of Omega k when writing that. The sign of k should be opposite. I'll correct the wording later.