# B Does the Universe have finite or infinite size?

1. Mar 20, 2016

### fxdung

At the time of Big Bang the size of Universe equal the size of an atom.The Universe has expanded and the time from the Big Bang to the present is finite.Then at the present time the size of the Universe is finite or infinite?

2. Mar 20, 2016

### andrewkirk

Not necessarily. If the universe is currently bounded (finite), it will have been very tiny at the time of the early Big Bang. But if it is currently unbounded (infinite) then it will have always been infinite - no matter how far we go back in time.

At least, that's the implication of the currently accepted cosmological theories.

Whether the universe is bounded or unbounded is unknown.

3. Mar 20, 2016

### newjerseyrunner

Way less actually, but that's not the point, this is incorrect. The observable universe was smaller than an atom, it was just denser, the universe may be and always have been infinite.

4. Mar 20, 2016

### fxdung

If universe always have been infinite,then how can we say about the beginning of space-time(therefore the beginning of time)?Is it because the gravity force very lage,so the space time was curved to zero?It seems there is contradictions:zero space-time but universe infinite?Are there two type of space-time:the space-time of observable universe that had the beginning and the space-time of whole unbounded universe(if universe is unbounded)?

Last edited: Mar 20, 2016
5. Mar 20, 2016

### phinds

Yes, it has one or the other, we just don't know which.

6. Nov 27, 2017

### Buzz Bloom

Hi phinds:

Although this thread is 18 months old, the same point seems to recur, as in #48 of
I am wondering if it is possible for us to agree that some aspects of science are "known", and the remainder aspects cannot be known ever.
Category 1: Knowable and known. Example: For phenomena taking place over extremely large spaces, General Relativity produces more accurate predictions than Newtonian physics.
Category 2: Unknown and unknowable. Example: Is the universe finite or infinite?

With respect to example (2), it will generally be possible as time passes to have some degree of confidence greater than 0.5 that (a) the universe is more likely to be finite, or (b) more likely to be infinite. If I remember correctly from past reading, there was no time during the past 100 years during which the general scientific consensus was (a). Since the early 20th century it has always been (b) or undecided. The confidence level will never be 100% for any category 2 knowledge.

I found the following 2005 paper which gives a basis for calculating a probability that the universe is infinite.
On the first page is the equation:
ΩT,0 = 1.02 +/- 0.04 .​
I understand that ΩT = ΩM + ΩΛ , where ΩM is the matter density, and ΩΛ is what may be called the "dark energy density". (It is assumed that the radiation density is negligible.) This means that statistically possible values for ΩK, the "curvature density", has a mean of -0.02 and a standard deviation of 0.04. Based on this assumed Gaussian distribution, the probability that the universe is infinite is
PROB {ΩK <= 0} = 0.84.​
My research skills are not very good, and I have not been able to find more recent corresponding data.

So, can we agree that it is OK to say that based on the 2005 data used in the cited paper, (1) the best probability estimate that universe is infinite is 84%, and (2) that no matter how much better new data becomes, this estimate will never become 100%?

Regards,
Buzz

Last edited: Nov 27, 2017
7. Nov 27, 2017

### phinds

I can't think of any way that we could ever know for sure that the universe is infinite. I think it is possible that future discoveries, refinement of measurements, and improved models could well put the likelihood NEAR 100% but our inability to go to infinity and look makes it, I think, impossible to ever say it's 100%

8. Nov 27, 2017

### Buzz Bloom

Hi phinds:

I think we agree then about my (2). What I am not sure about is whether you agree it is OK to say (based on (1)) something like:
"The universe is infinite with 84% certainty,"​
or
"Based on 2005 data, the universe is infinite with 84% certainty."
BTW, I found some newer data based on Plank 2015, but I am not sure how to interpret it probabilistically.
The top line of Table 5 on page 32 is about ΩK. There are values based on six different models, all but one with an unsymmetrical 95% confidence error range.

Regards,
Buzz

Last edited: Nov 27, 2017
9. Nov 27, 2017

### Bandersnatch

Isn't the probability of finding any particular value in a continuous distribution 0?

10. Nov 27, 2017

### Buzz Bloom

Hi Bandersnatch:

As I understand your question, the answer is YES, but it is not relevant. The 84% probability value is the area under a Gaussian probability distribution curve from -∞ to 0 with mean -0.02 and standard deviation 0.04.

Regards,
Buzz

11. Nov 27, 2017

### phinds

I'd be hesitant to put a number on it. I'm only comfortable with saying that it by far the most likely characteristic based on our current understanding of cosmology.

12. Nov 27, 2017

### andrewkirk

Are you perhaps thinking of a different question - whether the universe is flat? That corresponds to a zero curvature constant which is, as you say, a single value in a continuous range of possible values. As you suggest, that would be problematic because I don't think there is any way we could ever even put a probability on that.

But the question of whether the universe is infinite is whether the curvature constant is less than or equal to zero - ie hyperbolic or flat. That doesn't require estimating probabilities of a single value but rather of a range: $(-\infty,0]$.

13. Nov 27, 2017

### Bandersnatch

Yes, thanks Andrew and Buzz. I see it now.

14. Nov 28, 2017

### rootone

I say without any reason that it's finite; but so big that it might as well be infinite.

15. Dec 2, 2017

### Chronos

I prefer the abbreviated form of Phinds answer: Is the universe finite or infinite - Yes.

16. Dec 2, 2017

### phinds

So, now you have to say what shape it is

17. Dec 2, 2017

### rootone

Something like a Möbius strip but in more than two dimensions.
Well you did ask, it's not a personal theory or anything

18. Dec 2, 2017

### Staff: Mentor

Really? You have a valid reference (textbook or peer-reviewed paper) that explores the hypothesis that the universe is shaped like a Mobius strip (or its analogue in 4 dimensions)?

19. Dec 2, 2017

### rootone

No I don't, and it's not a hypothesis.
If I were a lot better at math than I am I might explore that though.

20. Dec 2, 2017

### Staff: Mentor

Then it's off topic here.