# The size of the universe at the big bang?

## Main Question or Discussion Point

So I read everywhere that everything was packed into an infinitely small space at the big bang. But then after some thousands of years the universe condensed enough to let electromagnetic waves travel through and these waves have been traveling 13.7 billion years to get here.
The problem here is of course is that electromagnetic waves travel at the speed of light, so it would seem they would have to start off 13.7 billion light years away for this to be possible.

Can this be because the universe has expanded so fast that this is possible?

Or is it because the universe was already infinite at the first instance after the big bang, but none the less has had everything grow further apart since then?

Marcus Post #20 in the balloon sticky answers that question pretty well. Short answer: Yes, the universe was expanding faster than the speed of light at that time.

phinds
Gold Member
So I read everywhere that everything was packed into an infinitely small space at the big bang
Then you did not read it in a refereed article but in some popularization, since it is not true

But then after some thousands of years the universe condensed enough to let electromagnetic waves travel through and these waves have been traveling 13.7 billion years to get here.
No, it EXAPANDED enough, not condensed, that the plasma fell out into matter and let the light through

The problem here is of course is that electromagnetic waves travel at the speed of light, so it would seem they would have to start off 13.7 billion light years away for this to be possible.
I don't know what you are getting at here. The earliest light we can see is about 13.7 billion years old and it was emitted at the time mention above (see "surface of last scattering" and "cosmic microwave backgound")

Can this be because the universe has expanded so fast that this is possible?
Again, I don't know what you mean.

Or is it because the universe was already infinite at the first instance after the big bang, but none the less has had everything grow further apart since then?
That is one model, and the generally preferred one at that but it is by no means certain. The universe might be finite but unbounded rather than infinite.

So I read everywhere that everything was packed into an infinitely small space at the big bang.
I read that a lot. It could be though that the Universe was both infinitely large and extremely dense.

If it is infinite in size now, then it was infinite in size then. If it is finite in size now, then it was finite in size then. How big was it in the finite case? Nobody knows. We are just guessing about that.

Chronos
Gold Member
The fact remains we do not know if the universe is finite or infinite. Both alternatives solve some problems, but, raise others.

The fact remains we do not know if the universe is finite or infinite. Both alternatives solve some problems, but, raise others.
OT. Not being bias here. Is there any way we can atleast make a probability, value without any certainty in which we can say that finite/infinite is morelikey suited explanation or vice versa (for now) based on findings and recent observations?

OT. Not being bias here. Is there any way we can atleast make a probability, value without any certainty in which we can say that finite/infinite is morelikey suited explanation or vice versa (for now) based on findings and recent observations?
There indeed is. The current data seem to favor a finite universe. If you believe their statistical analysis, and take their assumptions about the model to be true, then the probability that the universe is finite is about 93%. Usually in cosmology you start getting interested when the probability is 99.7% and begin to wait for a Nobel price when it's 99.9999%, so there is some way to go still.

There indeed is. The current data seem to favor a finite universe. If you believe their statistical analysis, and take their assumptions about the model to be true, then the probability that the universe is finite is about 93%. Usually in cosmology you start getting interested when the probability is 99.7% and begin to wait for a Nobel price when it's 99.9999%, so there is some way to go still.
Can you provide a reference for this 93% number ?

Can you provide a reference for this 93% number ?
Oh I forgot: http://arxiv.org/abs/1210.7231, page 14
... CMB+H0+BAO, is consistent with zero mean curvature at 1.5σ

There indeed is. The current data seem to favor a finite universe. If you believe their statistical analysis, and take their assumptions about the model to be true, then the probability that the universe is finite is about 93%. Usually in cosmology you start getting interested when the probability is 99.7% and begin to wait for a Nobel price when it's 99.9999%, so there is some way to go still.
It's instructive to look at historical measurements of the speed of light. For half of the experiments the actual value was outside of the 95% error bars.

Many of the early measurements of distances to heavenly bodies were off by a factor of two or more.

Oh I forgot: http://arxiv.org/abs/1210.7231, page 14
Sorry i was undere the impression that a flat universe is consistent with an infinite universe, sicne they have (even at low sigma) 0 mean curvature that would imply the universe is flat and hence possibly infinite.

http://www.astro.ucla.edu/~wright/cosmology_faq.html#RB

"Since we can only look at small piece of an object that has a large radius of curvature, it looks flat. The simplest mathematical model for computing the observed properties of the Universe is then flat Euclidean space. This model is infinite, but what we know about the Universe is that it is really big.
"

Oh I forgot: http://arxiv.org/abs/1210.7231, page 14
The conclusion of the article seems to be that the curvature is compatible with flat universe. How does that rule out infinite universe?

The conclusion of the article seems to be that the curvature is compatible with flat universe. How does that rule out infinite universe?
Yes. It seems flat universe offers a more decent probability than any of the other model and fits highly to land and balloon based experiment except for mathematical conclusion of infinite.

(http://map.gsfc.nasa.gov/universe/uni_shape.html).

How about the model of Aslanyan regarding torus model inserting both finite and infinite dimensions. Any latest finds?

The conclusion of the article seems to be that the curvature is compatible with flat universe. How does that rule out infinite universe?
Who said anything about ruling out anything?

Sorry i was undere the impression that a flat universe is consistent with an infinite universe, sicne they have (even at low sigma) 0 mean curvature that would imply the universe is flat and hence possibly infinite.

http://www.astro.ucla.edu/~wright/cosmology_faq.html#RB

"Since we can only look at small piece of an object that has a large radius of curvature, it looks flat. The simplest mathematical model for computing the observed properties of the Universe is then flat Euclidean space. This model is infinite, but what we know about the Universe is that it is really big.
"
That is of course true. My point was not to argue that they prove the universe is finite. What I meant is that you can find a number for the probability, if you really want one. And the probability, according to their analysis, for the universe to be finite is 93%.

Who said anything about ruling out anything?
That is of course true. My point was not to argue that they prove the universe is finite. What I meant is that you can find a number for the probability, if you really want one. And the probability, according to their analysis, for the universe to be finite is 93%.
Sorry, I misunderstood you. But I still don't see how your claim follows from the paper you provided.

Marcus Post #20 in the balloon sticky answers that question pretty well. Short answer: Yes, the universe was expanding faster than the speed of light at that time.
That was very informative! Thank you.

Then you did not read it in a refereed article but in some popularization, since it is not true
Probably so.

No, it EXAPANDED enough, not condensed, that the plasma fell out into matter and let the light through
I obviously meant to say that matter condensed enough to let light through.

Anyway thanks for all the answers.

This might be dumb but it is just a thought. If we say the universe was infinitely small at the big bang, it should never be able to grow into finite size right? Just like an infinite size should not be able to contract into a finite size?

Sorry, I misunderstood you. But I still don't see how your claim follows from the paper you provided.
It follows from their analysis, whose details I do not know entirely. But the quote I mentioned before translates exactly into the claim. Basically you get an estimate for the probability distribution for the curvature density parameter $\Omega_K$. This distribution is roughly Gaussian. For a Gaussian distribution, the probability of being 1.5 standard deviations away from the mean is 7%. Hence the probability 100-7 = 93%.

It follows from their analysis, whose details I do not know entirely. But the quote I mentioned before translates exactly into the claim. Basically you get an estimate for the probability distribution for the curvature density parameter $\Omega_K$. This distribution is roughly Gaussian. For a Gaussian distribution, the probability of being 1.5 standard deviations away from the mean is 7%. Hence the probability 100-7 = 93%.
Thanks, now I understand where the 7% comes from. But I still don't get why negative curvature means finite universe. Can't infinite universe have negative curvature as well?

This might be dumb but it is just a thought. If we say the universe was infinitely small at the big bang, it should never be able to grow into finite size right? Just like an infinite size should not be able to contract into a finite size?
OK, pick any number greater than zero for your size of the Universe. It is greater than zero, so it isn't infinitely small.

You can say something loose like "the series 1, 1/2, 1/4, 1/8, 1/16... becomes infinitely small as the series progresses." But no specific number in the series is infinitely small.