# Does the big bang imply a finite universe

1. Mar 23, 2005

### Allday

One reason people believe in the big bang is that everything is receeding from everything else and if we run time backwards then everything is crunched together. Now the descriptions I've read usually refer to the early universe as a finite space filled with hot gas. My question is, if our current universe is the product of the inflation and then expansion of that early small space then how can it have expanded to the point of being infinite. Does this rule out the possibility of an infinite universe?

One slightly related question concerns the CMB. We are bathed in this radiation that was emmited by the universe when it was very uniform and hot. As the universe cooled it presumably stopped radiating as a black body at some point. So will there be a time when all the CMB radiation has passed us by? I havent really thought about the boundry conditions that the CMB radiation would be subject to at the boundry of a finite universe, but if anybody could explain that would be nice. I know there are many models out there, but Im wondering if some are completely eliminated by these considerations.

2. Mar 23, 2005

### Chronos

The matter density of the universe was greater in the past than it is now, but that does not mean it was finite. The same goes for the temperature. The CMB will continue to cool, but never reach absolute zero.

3. Mar 23, 2005

### SpaceTiger

Staff Emeritus
If the Big Bang, as we currently understand it, is correct, then the "universe" (using any definition of the term) must be finite. The observable universe is certainly finite.

The CMB permeates all space, so it won't "pass us by", as you say, but it will become increasingly diffuse and cold. I suppose one can imagine strange topologies and cosmological parameters that would lead to it becoming anisotropic or inhomogeneous, but that's not quite the same as what you're saying.

4. Mar 23, 2005

### marcus

I tend to agree with Chronos on this point, and disagree with you SpaceTiger, but I am curious as to your reasoning.

As I (at least) currently understand the Big Bang, it does not require the universe to be finite.

I suspect that the universe MAY be finite. because the current estimate of Omega is just a hair bigger than one. and the error bounds are narrowing down.

But it is still possible that Omega =1 exactly. this is not out of the range of observational error.

And therefore I cannot rule out the possibility that the universe was spatially infinite at the moment it began to expand

5. Mar 23, 2005

### SpaceTiger

Staff Emeritus
It may be spatially infinite, but my usual understanding of the term "infinite universe" implies an infinity of time as well. Big Bang cosmology assumes otherwise. It would be bounded on one end.

6. Mar 23, 2005

### Allday

This is interesting. Im starting to think my two questions may be more related than I originally thought. Lets say the distance that CMB photons that we observe at a given time have travelled a distance r(t). In the scenarios where an infinitesimal amount of time after the big bang the universe was spatialy infinite, then I can see how there will always be CMB photons around they will just become more redshifted. The CMB photons will have filled an infinite space and as the space expands they will still fill it. If the universe is finite then as time goes on, dont we have to look farther back, ie doesnt r(t) increase with increasing t. And if so at some time wont we reach a time where r(t) has exceed the 'radius' of the observable universe (I think here is the only place I want to use observable instead of universe as a whole). Because doesnt the boundry of the observable universe as far as observations on earth are concerned constitute a boundry that things can disappear over?

Maybe this line of reasoning will work. In effect, there is no place for the CMB photons to go. If there is no edge or boundry to the universe (at least none that dont have periodic boundry conditions) and if all space was at some point filled with the material that emmitted the CMB photons then they will always be here. Does that sound qualitativly correct?

I suppose with a little bending of the imagination it is possible to think about a bang that happened everywhere at once in an infinite space. That seems OK. I was worried about something finite expanding to become infinite.

Last edited: Mar 23, 2005
7. Mar 24, 2005

### chronon

When we see the CMBR we are seeing the matter in the universe just before in cooled enough to become transparent - about 400000 years after the big bang, known as the time of decoupling. (see http://en.wikipedia.org/wiki/Cmbr)

If the universe is inifinite and there is no cosmological constant then we will go on seeing a CMBR forever, as we get to see matter from the time of decoupling but ever further away from us.

If the universe is infinite and the expansion is accelerating (positive cosmological constant) then the matter at the time of decoupling will eventually cross our cosmological event horizon, and we won't see CMBR any more.

If the universe is finite then we will carry on seeing the CMBR, which will go round and round the universe, although the big crunch is likely to happen first.

You may also be interested in my web page: http://www.chronon.org/Articles/cosmichorzns.html

8. Mar 26, 2005

### Allday

thanks

9. Mar 27, 2005

### SpaceTiger

Staff Emeritus
I don't think that's right. The CMBR permeates all space, so the event horizon doesn't apply here. The event horizon refers to the comoving distance beyond which we will never see, but decoupling didn't happen at some large comoving distance, it happened everywhere (a long time ago). Although there may come a time when the expectation value for the number of CMB photons in our observable universe is less than 1, the field should still permeate all space, acceleration or no.

10. Mar 28, 2005

### chronon

Sorry you're right. I think of the CMBR in the same way as light from a distant galaxy. For a positive cosmological constant, such a galaxy will eventually disappear behind a cosmological event horizon - that is we won't see it after a given time in its history. However, we will go on seeing it before that time, getting more and more redshifted. Likewise, in the case of the CMBR, at present we see radiation from matter that is further and further away as time passes, but eventually we won't see it from any further away, but from the same distance, and becoming more redshifted.

11. Mar 28, 2005

### marcus

thanks so much to both of you chronon and SpaceTiger for elucidating this, it is a very interesting question how the CMB will eventually look and if we will see it at all etc.
I was thinking about it too but never got around to contributing to this thread.

cosmologists talk about the 'surface of last scattering' which is the geometric locus of where the CMB photon decoupled and got loose to fly thru essentially transparent space. and it is a spherical surface around us currrently at distance z = 1100
as time goes on this surface apparently gets farther away

Lineweaver has some analogies about this in his "Inflation and the CMB" paper from back in 2003.

dont know if this is useful to you.

12. Mar 29, 2005

### moving finger

The surface is getting further away, yes, but our event horizon relates to events in spacetime, not to objects or surfaces in space. The 'last scattering' represents a spacetime event in the past which is within our event horizon, and since (as an event) it is within our event horizon it will always be within our event horizon, at all times in the future, hence we will always see the CMB. I know this is tricky to understand, I'm always conused by it and I'm not even sure I have explained it properly myself, but take a look at
http://vega.bac.pku.edu.cn/rxxu/cosmos/cosmology-inflation03.pdf
which has a very good explanation and diagrams.

MF

I realised that if I understood too clearly what I was doing, where I was going, then I probably wasn’t working on anything very interesting

13. Mar 29, 2005

### Mike2

Can the redshift of z=1100 indicate how large the entire universe is? If we know how large it was a the time of last scattering, and we know how much it has redshifted, then does that give us how much it has expanded?

14. Mar 29, 2005

### SpaceTiger

Staff Emeritus
The redshift, "z", automatically gives the amount by which the universe has expanded:

$$1+z=\frac{a_0}{a}$$

where $$a_0$$ is the scale factor now and $$a$$ is the scale factor at recombination. Unfortunately, simple observations of the CMB can't tell us how large (in physical units) the universe was at recombination. More complex analysis of the power spectrum can give us cosmological parameters, which can in turn lead to the physical scales of the universe. That's exactly what WMAP did recently.

Last edited: Mar 29, 2005
15. Mar 29, 2005

### marcus

the link is to Lineweaver and Davis "Expanding Confusion", a really good article. it shares some content and diagrams with one I cited earlier by Lineweaver called "Inflation and the CMB"

here is an interesting quote from Lineweaver and Davis page 9 section 3.3:

"...Although the last scattering surface is not at any fixed comoving coordinate, the current recession velocity of the points from which the CMB was emitted is 3.2c (Fig. 2). At the time of emission their speed was 58.1c, assuming (Omega_M, Omega_Lambda) = (0.3, 0.7). Thus we routinely observe objects that are receding faster than the speed of light and the Hubble sphere is not a horizon..."

here is an alternative link to Lineweaver Davis, from the one MF gave
http://arxiv.org/abs/astro-ph/0310808

Last edited: Mar 29, 2005
16. Mar 30, 2005

### Mike2

Didn't last scattering occur 300,000 years after the initial big bang? Does that give us a last scattering size of the universe at 300,000 light years across? Or could some portions of the universe have been expanding from other portions faster than light?

17. Apr 4, 2005

### moving finger

Yep, exactly the latter (my emphasis). There is nothing to prevent expansion of space at "speeds" greater than the speed of light (this is exactly how inflation is supposed to have solved the horizon problem in the first place). At all times in the past, present and future there can be parts of space which are expanding relative to each other at "speeds" greater than the speed of light.

For this reason, our universe could be infinite in size (and thus always has been infinite in size), yet still expanding according to "Hubble's law".

MF

18. Apr 4, 2005

### SpaceTiger

Staff Emeritus
Sorry, I guess I overlooked this post before. Actually, the age of the universe is not the same as the observable size because everything is considered in comoving coordinates. Why? Well, hopefully this example will help:

Imagine that the universe is just created and it's infinite in extent. Also, to start, let's imagine that it's not expanding (steady state). How large is your observable universe at a given time? Well, it's simply the distance that light could travel since the beginning of time. In this case, your above assumption would be right.

However, the universe is not stationary, it's expanding. In this case, when you talk about the observable universe, you want to talk about the amount of "stuff" that you've seen since the beginning of time. The stuff is expanding away from you, however, so you want to choose a frame in which it's stationary. This is the "comoving" frame. Thus, the relation between the age of the universe and the particle horizon is:

$$a_{particle}=\int \frac{c}{a}dt$$

where "a" is the scale factor, a measure of how large the universe at a given time. You can see that when "a" is a constant, then the size of the universe is just the speed of light times the age.

19. Apr 4, 2005

### Mike2

I wonder, if the density of matter is related to the expansion rate, then the universe could still be infinitely big and infinitely old. When things expand then matter leaves our cosmological event horizon and the density of the observable universe decreases. This may cause the rate of expansion to increase causing the event horizon to shrink and even more matter to disappear and the universe to become even less dense. At some point there is very little matter if any, the universe is expanding very rapidly, the cosmo event horizon is very small and a greater proportion of virtual pairs are separated more easily since one of them slips behind the now very small event horizon. This creates a great influx of new matter slowing the universe down, expanding the cosmo event horizon allowing galaxies to form. But since it is always expanding, there is always matter disappearing, ensuring that the cycle of big bangs of matter followed by galaxy evolution followed by expansion acceleration followed by a big rip that creates another big bang. The question is: What observation prevent this scenario?

20. Apr 5, 2005

### moving finger

If the universe is infinitely old then we would receive photons from every star in the universe, no matter how far away or how fast they are receding from us. If the universe is also infinitely large then effectively no matter where you look, your line of sight would end on a star. This would mean the night sky should be ablaze with light. The night sky is observed to be NOT ablaze with light, hence we conclude the universe cannot be both infinitely old and infinitely large (Olber's paradox).

The universe could however be infinitely large and finitely old, or infintely old and finitely large.

MF