Does the big bang imply a finite universe

[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 haven't 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 I am wondering if some are completely eliminated by these considerations.

 

[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.

 

[SpaceTiger]

Does this rule out the possibility of an infinite universe?

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.

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?

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.

 

[marcus]

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.

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

 

[SpaceTiger]

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

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.

 

[Allday]

follow up

This is interesting. I am starting to think my two questions may be more related than I originally thought. Let's say the distance that CMB photons that we observe at a given time have traveled 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, don't we have to look farther back, ie doesn't r(t) increase with increasing t. And if so at some time won't 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 doesn't 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 don't 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.

Thanks for the comments

 

[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

 

[Allday]

thanks

thanks for the links chronon. they were helpfull

 

[SpaceTiger]

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.

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.

 

[chronon]

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.

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.

 

[marcus]

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,...

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.

 

[moving finger]

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

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

 

[Mike2]

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.

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?

 

[SpaceTiger]

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?

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.

 

[marcus]

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.

...

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

 

[Mike2]

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.

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?

 

[moving finger]

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?

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

 

[SpaceTiger]

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?

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.

 

[Mike2]

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

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?

 

[moving finger]

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.

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 infinitely old and finitely large.

MF

 

[hellfire]

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).

I did already comment this in another thread. There are two possibilites to avoid Olbers’ paradox in an eternal and spatially infinite universe. 1. If space expands 2. If the matter follows a fractal distribution with fractal dimension less than two (this is actually not the case for very large scales).

 

[Mike2]

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 infinitely old and finitely large.

MF

I'm not committed to this view, of course. But if space is expanding, then there is a distance at which the space is receding from us faster than light. That means, any photon beyond that point will never reach us, no matter where or how long ago it was emitted. The speed of the photon is fixed at c, and the distance to that point is increasing faster than c. So we would not see light from everywhere in space if space is expanding and there is a cosmological event horizon.

So the question still remains, can big bangs be caused by a very low density of matter giving rise to a very fast expansion rate which shrinks the cosmological event horizon to such a small size that very many virtual pairs of the quantum foam are separated when they slip behind the very close cosmological event horizon, leaving behind permanent matter in large quantities?

Some pose that the CMB proves an initial big bang and subsequent expansion. I don't disagree. I'm suggesting that there may be more than one big bang and more than one CMB created each time the universe experiences a big rip. In other words, a big rip causes a new big bang with all the characteristics of the one we see now. Is there any observable evidence that can disprove this big rip = big bang theory? Thanks.

For example, perhaps if it can be shown that the curvature of the universe is not flat, but consistent with the curvature of an initially tightly curled universe that is in the process of unfurling, then that would prove that we are in an the first and ony big bang. If it can be shown that the universe is exactly flat, then we must have been expanding forever, right?

 

[hellfire]

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...

I don't understand what you are trying to say here, but I think I can clarify one thing: in an universe filled only with matter and radiation the expansion of space will always decelerate. If space is flat or open deceleration will be smaller as time passes, but it will be never become an acceleration. You can prove this making use of the second Friedmann equation and the definition of the deceleration parameter.

 

[matt.o]

I'm not committed to this view, of course. But if space is expanding, then there is a distance at which the space is receding from us faster than light. That means, any photon beyond that point will never reach us, no matter where or how long ago it was emitted. The speed of the photon is fixed at c, and the distance to that point is increasing faster than c. So we would not see light from everywhere in space if space is expanding and there is a cosmological event

This is a common misconception. Galaxies receding at faster than light speeds can still be observed by us. If you think about it a little it will become clear. Consider a galaxy traveling with the Hubble flow at such a distance that it is receding at faster than the speed of light. Now consider a point half way between us and the FTL galaxy. The recessional velocity here is not FTL, wrt us and the FTL galaxy. Hence light can get to this midway point from the FTL galaxy. If light can get to the midpoint, then it can also get to us. If you search for Tamara Davis and Charlie Lineweaver on google scholar or ADS, then you will come up with references on FTL recession.

Some pose that the CMB proves an initial big bang and subsequent expansion. I don't disagree. I'm suggesting that there may be more than one big bang and more than one CMB created each time the universe experiences a big rip. In other words, a big rip causes a new big bang with all the characteristics of the one we see now. Is there any observable evidence that can disprove this big rip = big bang theory? Thanks.

This is very hard to prove or disprove. I would suggest that there could be no observational evidence since the big rip occurred before the big bang (hence unobservable to us).

For example, perhaps if it can be shown that the curvature of the universe is not flat, but consistent with the curvature of an initially tightly curled universe that is in the process of unfurling, then that would prove that we are in an the first and ony big bang. If it can be shown that the universe is exactly flat, then we must have been expanding forever, right?

Current evidence suggest the density parameter is very close to 1, hence the Universe is flat. However it is not true that we must have been expanding forever if the Universe is flat.

Matt.

 

[turbo]

I did already comment this in another thread. There are two possibilites to avoid Olbers’ paradox in an eternal and spatially infinite universe. 1. If space expands 2. If the matter follows a fractal distribution with fractal dimension less than two (this is actually not the case for very large scales).

Olber's paradox can also be very easily avoided even in an infinite (spacially and temporally) universe if light loses energy through interaction with the EM fields through which it passes. Light will be progressively redshifted, eventually being redshifted into undetectability. Indeed the universe is bright at these very long wavelengths (CMB).

 

[Mike2]

This is a common misconception. Galaxies receding at faster than light speeds can still be observed by us. If you think about it a little it will become clear. Consider a galaxy traveling with the Hubble flow at such a distance that it is receding at faster than the speed of light. Now consider a point half way between us and the FTL galaxy. The recessional velocity here is not FTL, wrt us and the FTL galaxy. Hence light can get to this midway point from the FTL galaxy. If light can get to the midpoint, then it can also get to us. If you search for Tamara Davis and Charlie Lineweaver on google scholar or ADS, then you will come up with references on FTL recession.

Yes, but by the time the light from the FTL galaxy reached the half-way-point galaxy, the half-way-point galaxy would be beyond the cosmological event horizon as well.

Originally Posted by Mike2
Some pose that the CMB proves an initial big bang and subsequent expansion. I don't disagree. I'm suggesting that there may be more than one big bang and more than one CMB created each time the universe experiences a big rip. In other words, a big rip causes a new big bang with all the characteristics of the one we see now. Is there any observable evidence that can disprove this big rip = big bang theory? Thanks.

This is very hard to prove or disprove. I would suggest that there could be no observational evidence since the big rip occurred before the big bang (hence unobservable to us).

One thing that may end the big-rip = big-bang scenario is this: if the quantum fluctuation are not scale invariant, then the scale factor of space cannot expand forever to create big-bangs over and over again. If particles are extended objects, then this cannot happen. If particles are singularities, then this might still happen unless the path-integral formulations are not scale invariant. What do you think?

 

[Chronos]

I wonder if a different analogy would help demystify FTL expansion. If a jet plane flew past you traveling in excess of the speed of sound, would you hear it as it receeded into the distance?

 

[matt.o]

Mike2, you should just go and find the papers by Davis and Lineweaver.

 

[moving finger]

Yes, but by the time the light from the FTL galaxy reached the half-way-point galaxy, the half-way-point galaxy would be beyond the cosmological event horizon as well.

matt.o is right, Mike2. The recession velocity of stellar objects makes no difference as to WHETHER the light from these objects will reach us or not; the distance and recession velocity only makes a difference to WHEN the light from these objects reaches us. If a spacetime event is beyond our event horizon then the light from that event will not reach use before the "end of time"; but all objects in a universe which is infinitely old were within our event horizon at some stage during the past, therefore we will receive light from all of those objects today.

MF

 

[Mike2]

...If a spacetime event is beyond our event horizon then the light from that event will not reach use before the "end of time"; but all objects in a universe which is infinitely old were within our event horizon at some stage during the past, therefore we will receive light from all of those objects today.

The first sentence agrees with me that if there is a cosmological event horizon, then we will never see objects beyond it. Or what else can "before the 'end of time'" mean?

Inflation predicts an exponential expansion rate in the early universe. This means that the universe could have approached an infinitely small singularity in the infinite past. In other words, then universe may be infinitely old. We don't know how long the universe existed before inflation. Yet we may still have an event horizon in this universe.

If distance is increasing faster than an object is moving, it will never reach us. If you roll a ball eastward at 5mph on an infinitely long train moving westward at 6mph, the ball is actually moving away from a stationary observer behind the ball at 1mph. What?