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Words escape me, but by "whole universe" (I think) I mean everything that's spatially connected to the observable universe in a conventional sense. If there is a better term for it, please let me know!

I was surprised to find out that theories and measurements about the big bang seem to mostly relate to the size of the observable universe via expansion, and if I understand correctly don't say much about the size of the whole universe.

Have I got this right? Are there any ways at all to try to estimate size of the whole universe? Does the term even mean anything?

See @RobJeffries' excellent answer to When will the number of stars be a maximum? and @Acccumulation's comment for background on this question.

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  • $\begingroup$ If you can't observe something you certainly can't measure it and if you can't make relevant measurements you cannot verify a theory. Without data to base a theory on you aren't doing much more than making an elaborate guessing. $\endgroup$
    – StephenG - Help Ukraine
    May 7, 2019 at 1:28
  • $\begingroup$ @StephenG In science we can use one kind of data to formulate a theory that predicts a different kind of data. I think that there are numerous examples of predictions which precede measurements. General Relativity and all its implications might be a good example of that. "We can't measure it so we can't predict or even estimate it" is an oversimplification. $\endgroup$
    – uhoh
    May 7, 2019 at 1:32
  • $\begingroup$ There are unfortunately lots of theories which have proven wrong because later measurement proves them wrong. For every theory that is proven right (or more accurately right within acceptable error) there are many, many more that sounded perfectly reasonable but when they were eventually testable, proved wrong. Prediction alone is not enough. $\endgroup$
    – StephenG - Help Ukraine
    May 7, 2019 at 1:37
  • $\begingroup$ @StephenG I haven't asked for "right theories". In fact, I don't think there is such a thing. Usually there are theories that seem to work, and ones that don't. Here in my question though, I've only asked "Are there any ways at all to try to estimate..." $\endgroup$
    – uhoh
    May 7, 2019 at 5:01
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    $\begingroup$ Major limitation is that the current understanding poses that out of the realm of physics. I think the proper term is unfalsifiable. Cosmology has indeed a special status, beyond a limit it cannot go. Which will always give room to philosophical questions. $\endgroup$
    – Alchimista
    May 8, 2019 at 8:58

2 Answers 2

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tl; dr The universe is probably infinite, but if that's the case it's impossible to verify. If the universe is finite, and small enough, and the global curvature is equal to the curvature of our observable universe, then we will be able to estimate its size.

If the global curvature of the universe isn't positive, then the size of the universe is infinite, (and it's always been infinite since the dawn of time, at the Big Bang), assuming the topology of the universe is trivial.

Measurements of the observable universe indicate that the curvature may be zero (giving a flat universe), or even negative; if the curvature is positive, then its value is very small. We assume that the observable universe is typical of the whole universe, but of course that's impossible to verify.

Wikipedia says that

experimental data from various independent sources (WMAP, BOOMERanG, and Planck for example) confirm that the observable universe is flat with only a 0.4% margin of error.

[...]

The latest research shows that even the most powerful future experiments (like SKA, Planck..) will not be able to distinguish between flat, open and closed universe if the true value of cosmological curvature parameter is smaller than $10^{-4}$. If the true value of the cosmological curvature parameter is larger than $10^{-3}$ we will be able to distinguish between these three models even now.

So even if the total universe does have positive curvature, its size is much larger than the observable universe, assuming that our observable universe isn't a patch that's abnormally flat.

According to How Big is the Entire Universe? by Ethan Siegel, if the curvature is positive, then the diameter of the total universe is at least 14 trillion lightyears, but that article is from 2012, more recent calculations may give a larger value.

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  • $\begingroup$ Let us continue this discussion in chat. $\endgroup$
    – PM 2Ring
    May 7, 2019 at 6:52
  • $\begingroup$ The tl;dr is very helpful, thank you! I'm not a cosmologist and so it is helpful to have guide where the explanation is going to go before diving in, and I am sure it's going to be helpful to some future readers as well! $\endgroup$
    – uhoh
    May 7, 2019 at 6:58
  • $\begingroup$ Ah, I hadn't noticed that! Perhaps this is more like playing chess than logic ;-) $\endgroup$
    – uhoh
    May 10, 2019 at 2:18
  • $\begingroup$ omg physics SE is a whole 'nuther universe. It's an angsty place, but much better than several years ago. There was a "thing", and it's been improving ever since. I think there are very different ways to handle low question-rate sites and high question rate sites. stats: Physics: 92/day, Astronomy: 5/day Personally I think Physics SE should be broken up, slower Q/day lowers angst and that is particularly useful to encourage new users to stick around and grow with the site. SO is yet a whole 'nuther 'nuther but is also thankfully in "angst-recovery". $\endgroup$
    – uhoh
    May 10, 2019 at 2:39
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    $\begingroup$ @uhoh If the OP clarifies that Moon question, or at least gives some feedback, I'll vote to reopen it. $\endgroup$
    – PM 2Ring
    May 10, 2019 at 4:17
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So far our estimates of the size of the Universe is from what it is expected to be (i.e. calculations) rather than what we see. But there are several problems.

Age of the Universe

We are pretty sure of the age of the Universe, 13.8B years old, and the time when the first light was emitted. This gives us a relatively good idea of the size of the Universe since we consider that the furthest edge of our Universe is the light that it has emitted so far which has gone outward and never hit anything.

Assuming a perfect sphere, a.k.a. a perfect Euclidean Universe (which it isn't,) then you would think the Universe is a sphere with a radius of about 13.8 billion light years and so its size would be:

$$size_{universe} = {\frac {4 \pi \times r^3} {3}}$$

With r = 13.8 billion light years.

Hubble Discovery: Expansion of the Universe

Only we know that our Universe is in expansion and there is nothing that says it's going to stop expanding. This affects the size of the Universe. Unfortunately, when we look around the cosmos, we can't see the expansion happening. We inferred it because of what we call the redshift. Most of the far away galaxies are moving away from us, the further they are, the longer the wave length of their light.

The speed at which the expansion happens is not yet set in stone either. Therefore, we have many arguing about the current size of the Universe.

Is there an Horizon?

One problem we currently have is the weight of the observable Universe. We calculated a weight which is much higher than what we see... so we added Black Matter. Matter which we can't see because it doesn't emit any kind of radiation and it's not a small weight: 85% of the calculated weight is missing!

Another theory, in that regard, is the possibility that the Expansion of the Universe has already moved most of the would be visible Universe over the Horizon.

When you go to the Ocean and look at the water, at some point you see the edge of the Earth. This is called the Horizon. Whatever is behind that line, you can't see it unless you go toward the horizon (when we observe the Universe, though, we stay in our solar system...) At such a size, the Universe is expanding faster than the speed of light. So light over the Horizon will never reach us because it can't go faster than the Expansion.

One more theory which is going to be hard to prove...

Limited Size?

There is a funny word circulating these days: Circumnavigation. This is like Pacman going out on the left side of the screen to re-appear on the right side. There are theories, which so far have been disproved, that the Universe would be finite and that things going in one direction reappear in on the other side. (If I'm correct, this is directly linked to the string theory.)

I guess some people think that this would have been great since that would mean our Universe has a specific size and things will always be around. They just float and go around, come back where they were... in an infinite loop.

So far, we have not been able to see light of galaxies coming from the opposite direction. This is also quite contradictory with the possibility of a Horizon.

I also personally think this is contradictory with the Expansion theory. If the Universe had a limited size, how could it also expand?

So what's the size?

We actually calculate a size from what we can observe using a radius of 46.5 billion light years. This gives us an estimation of

$$3.57×10^{80} m^3$$

This size takes our best estimate of the redshift in account.

For additional details about how the size is calculated, I would suggest reading the Size of the Observable Universe section on Wikipedia.

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  • $\begingroup$ Well I recommended something a little shorter but okay, thank you! $\endgroup$
    – uhoh
    May 10, 2019 at 8:58
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    $\begingroup$ @uhoh, I know. I just couldn't see how to get the answer without proper explanations... $\endgroup$
    – Alexis Wilke
    May 10, 2019 at 15:40

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