B Estimates — True Size of the Universe?

[Ascendant0]

TL;DR Summary

Looking to see if there are any estimates based off our cumulative understanding of the universe, how large it is overall?

I always thought it was odd that we know dark energy expands our universe, and that we know it has been increasing over time, yet no one ever expressed a "true" size of the universe (not "observable" universe, the ENTIRE universe) by just reversing the process of expansion based on our understanding of its rate through history, to the point where everything would've been in an extremely small region. The more I've looked into it recently, I've come to find that it is due to that "inflation" period within the first few fractions of a second after the Big Bang, where the expansion rate defies our currently understood laws of physics, and so we don't know what could've happened - from a given minimum based on all we've seen of the observable universe to date, but upwards to a maximum of infinity?

So from what I gather, so little is understood about that "inflation" period that we have absolutely no clue how truly large the universe is overall? Has there never been any estimates that seemed to have any fair basis of reasoning within our current understanding? I have looked around the web, asked four different AI (which I know oftentimes doesn't have the latest material), and can't seem to find anything or anyone even willing to guess at it.

I respect that no one wants to just make up numbers, but I am curious as to whether anyone filled in that gap to a feasible extent that gave us even a remote idea of the size of the universe? This is excluding any claims that aren't accepted by the scientific community - something that would be solid enough for many scientists to say it's feasible? If so, where can I find this information, and what was that size estimated to be?

 

[PeroK]

TL;DR Summary: Looking to see if there are any estimates based off our cumulative understanding of the universe, how large it is overall?

I always thought it was odd that we know dark energy expands our universe,

The universe expands because a static universe is not compatible with General Relativity. The universe must either be expanding or contracting; it cannot be static.

Dark energy, which is the energy of the vacuum, is now thought to be driving an accelerating expansion. Without dark energy, the universe expansion should be slowing down.

and that we know it has been increasing over time, yet no one ever expressed a "true" size of the universe (not "observable" universe, the ENTIRE universe) by just reversing the process of expansion based on our understanding of its rate through history, to the point where everything would've been in an extremely small region.

All we know is that the universe is significantly larger than the observable universe. I think current measurements estimate the size of the whole universe to be at least 100 times the diameter of the observable universe. In fact, it's so large that there is no evidence that it has a finite size. It could be spatially infinite. And, the best current model has a working assumption that it infinite.

The more I've looked into it recently, I've come to find that it is due to that "inflation" period within the first few fractions of a second after the Big Bang, where the expansion rate defies our currently understood laws of physics, and so we don't know what could've happened - from a given minimum based on all we've seen of the observable universe to date, but upwards to a maximum of infinity?

If the universe is infinite, then it has always been infinite. It started in a hot dense state - but that would still have been a spatially infinite hot dense state.

So from what I gather, so little is understood about that "inflation" period that we have absolutely no clue how truly large the universe is overall?

As above, there is an estimate of its minimum size and a hypothesis that it is infinite.

Has there never been any estimates that seemed to have any fair basis of reasoning within our current understanding? I have looked around the web, asked four different AI (which I know oftentimes doesn't have the latest material), and can't seem to find anything or anyone even willing to guess at it.

There's an article here:

https://www.space.com/24073-how-big-is-the-universe.html

 

[Ibix]

There are three classes of solution to the Friedman Equations - closed, flat and open. Flat and open universes are infinite in extent and always were. Closed universes do have a definable size. Unfortunately our measurements of our universe don't rule out any of the models.

If our universe is closed, though, it's big. The minimum possible size consistent with our measurements has a diameter around 100 times that of our observable universe, from memory.

 

[Hornbein]

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

"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.

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

That's a minimum of 50 times the volume of our observable Universe.

 

[Bandersnatch]

There's an article here:

https://www.space.com/24073-how-big-is-the-universe.html

That's a bad article. They quote a paper that reports at least 250 Hubble volumes in our universe, and come up with 7 trillion light years across - apparently by multiplying the diameter of a Hubble volume by 250.
It's like asking: how big is your swimming pool? Well, I can fit 250 plastic balls in it, each 28 cm in diameter - therefore the pool is 250x28 cm = 70 metres across.
And what's this bit about: 'If the universe expanded at the speed of light during inflation'?
I'd stay away from it.

The minimum possible size consistent with our measurements has a diameter around 100 times that of our observable universe, from memory.

The same reference, mentioned above (Vardanyan et al.), reports 42 Gpc (136 Glyr) for the minimum radius of the curvature of the hypersphere, from which we get ~860 Glyr diameter of the 3d 'surface'. I.e. diameter-wise, less than 10 times larger than our observable patch.
In this thread: https://www.physicsforums.com/threa...mine-the-universes-size.1051357/#post-6901481 (shameless plug of my own post) we came up with 14 times the size by using a much less sophisticated method.

@Ascendant0 the estimates quoted above are coming from attempts to measure the curvature of the universe by looking at the cosmic microwave background. The assumption is that if the entire universe is finite, then it must curve on itself (it can't have edges), and if it does so in the simplest way possible - i.e. as a higher-dimensional sphere - then the measured curvature will tell you how big the hypersphere must be.

The actual numbers rely on error bars in the measurements - there's a range of possible actual values that could all show up as the same result due to the limitations of the measuring techniques. The results hover close to 0, corresponding to a flat infinite universe, but are imprecise enough to accommodate a slight positive curvature (as well as negative, but that's just another type of infinite universe, so let's ignore it).
The largest positive curvature (= smallest radius of curvature) that can hide in those error bars is what is used as the basis for the estimate of the minimum size of the universe.

You can take the number for the size of universe derived from this and say: as of current knowledge, the universe can be anywhere from about that size to infinitely large - unless the underlying assumption about it curving like a hypershpere is wrong, in which case you can't even say that.

 

[Jaime Rudas]

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

"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.

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

That's a minimum of 50 times the volume of our observable Universe.

Where do you get that it's 50 times the volume of our observable universe?

I ask this because, as I see it, if the radius of the observable universe is 46 Gly, its volume will be about 400 Tly³. On the other hand, if the radius of the entire universe is 170 Gly, its volume will be about 97 Ply³, and the ratio between these volumes will be 97 Ply³/400 Tly³ ≈ 240

 

[Hornbein]

Where do you get that it's 50 times the volume of our observable universe?

I ask this because, as I see it, if the radius of the observable universe is 46 Gly, its volume will be about 400 Tly³. On the other hand, if the radius of the entire universe is 170 Gly, its volume will be about 97 Ply³, and the ratio between these volumes will be 97 Ply³/400 Tly³ ≈ 240

Stupid me, I calculated for a 2D universe. This is generally believed to be nonphysical.

 

[Bandersnatch]

@Hornbein your calculation is for the Rc of a hyperbolic universe, as discussed in the thread you linked to.

 

[Jaime Rudas]

The same reference, mentioned above (Vardanyan et al.), reports 42 Gpc (136 Glyr) for the minimum radius of the curvature of the hypersphere, from which we get ~860 Glyr diameter of the 3d 'surface'. I.e. diameter-wise, less than 10 times larger than our observable patch.

Using more recent data, post #7 (adjusted in post #24) of this thread concludes that, if the universe is finite, its radius of curvature is at least 469 Gly, or about 10 times the radius of the observable universe. This implies that the volume of the entire universe is at least 4700 times the volume of the observable universe.

 

[Hornbein]

Using more recent data, post #7 (adjusted in post #24) of this thread concludes that, if the universe is finite, its radius of curvature is at least 469 Gly, or about 10 times the radius of the observable universe. This implies that the volume of the entire universe is at least 4700 times the volume of the observable universe.

The volume of a sphere is pi*4/3*r^3. When making a ratio the constants cancel out. Set the radius of the observable universe to 1. Then the unobserved universe has 10^3 more volume.

It appears the calculation I made with the older data was correct. (170/46)^3 =~ 50. Hah! First time I have ever used the tilde with this keyboard.

 

[Jaime Rudas]

The volume of a sphere is pi*4/3*r^3. When making a ratio the constants cancel out. Set the radius of the observable universe to 1. Then the unobserved universe has 10^3 more volume.

Yes, the volume of a ball is 4/3 πr³, but the volume of a 3-sphere is 2π²r³

Edit: the observable universe is a ball, while a finite universe would be a 3-sphere.

 

[Jaime Rudas]

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

"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.

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

In fact, what you're suggesting in that post doesn't take into account that positive curvature implies a negative $\Omega_{\kappa}$. Now, following your reasoning, if we use data (47b) from Planck 2018 results ($\Omega_{\kappa}=0.0007 \pm 0.0019$), we would find that the lowest value of $\Omega_{\kappa}$ would be:
$$\Omega_{\kappa}=0.0007 - 3 \times 0.0019= -0.005$$
So the minimum radius of curvature would be $R_c=14.5/\sqrt{0.005}$ near 200 Gly, which implies that the volume of the universe would be at least 380 times the volume of the observable universe.

 

[Hornbein]

In fact, what you're suggesting in that post doesn't take into account that positive curvature implies a negative $\Omega_{\kappa}$. Now, following your reasoning, if we use data (47b) from Planck 2018 results ($\Omega_{\kappa}=0.0007 \pm 0.0019$), we would find that the lowest value of $\Omega_{\kappa}$ would be:
$$\Omega_{\kappa}=0.0007 - 3 \times 0.0019= -0.005$$
So the minimum radius of curvature would be $R_c=14.5/\sqrt{0.005}$ near 200 Gly, which implies that the volume of the universe would be at least 380 times the volume of the observable universe.

That appears to be correct. I've learned something here.

 

[Jaime Rudas]

if we use data (47b) from Planck 2018 results ($\Omega_{\kappa}=0.0007 \pm 0.0019$)

From this, we could also conclude with 36% confidence that the universe has positive curvature and with 64% confidence that it has negative curvature.

 

[Orodruin]

From this, we could also conclude with 36% confidence that the universe has positive curvature and with 64% confidence that it has negative curvature.

Probability, not confidence. Cosmology analyses are generally Bayesian rather than frequentist.

 

[PeroK]

Probability, not confidence. Cosmology analyses are generally Bayesian rather than frequentist.

Or, "credence"?

 

[Hornbein]

Probability, not confidence. Cosmology analyses are generally Bayesian rather than frequentist.

That seems appropriate. It is hard to imagine the Cosmos as a repeatable experiment. Not yet anyway.

 

[Orodruin]

That seems appropriate. It is hard to imagine the Cosmos as a repeatable experiment. Not yet anyway.

Sure, but that's not why they do Bayesian analyses ...