CMB, The Horizon Problem and a comment on BH's

[superg33k]

How can we still receive photons from last scattering, i.e. the CMB? Does our receiving the photons (not other evidence from CMB) require a constraint on the curvature of the universe or the speed of expansion?

I can see how a curvature that described a closed universe would have CMB around forever (kinda like going off the edge of the screen in snake (old nokia phone game) and appearing at the opposite side). Alternatively if parts of the universe were expanding very close to (or greater than) the speed of light relative to us I can also see that we could still receive their photons. If neither a restriction on the curvature or rate of expansion is required, which I don't find mentioned in my books, then I can't see how we are still receiving CMB radiation.

It would be like our universe was an expanding balloon, all points shined a torch, very quickly all photons would be outside the balloon!

Another related problem I am having is The Horizon Problem. Does it require inhomogeneities from quantum processes?

My understanding is that the Universe at last scattering was about 100 (or 300 or 900, one of them) million light years across. The CMB shows that all 4/3 pi (100 million light years)^3 of it was all very much the same temperature. And this thermal equilibrium is very hard to achieve when parts of the universe have never been within each others particle horizon.

My issue are, wouldn't they have been within each others particle horizon when the universe was a lot smaller? Is it that the universe is expanding so close to (or faster than) c that some bits still won't be in each others particle horizon? Or is it that quantum fluctuations will have been expanded to greater fluctuations universe before last scattering and the CMB is even more isotropic than that? Or is it something else?

Finally, if the universe was a lot smaller and the same mass, why on Earth didn't it collapse into a black hole?

 

[Drakkith]

The CMB is EVERYWHERE. As space expanded over billions of years, the density of this CMB fell as did the temperature (energy) of the photons. These photons were created everywhere in the universe, so the ones created in our region of space 13+ billion years ago, are already far far away. We are simply receiving other photons from elsewhere now.

Also, while two points in space may be receding from each other at c+ NOW, we can easily receive photons generated in such a point BEFORE it was receding that quickly.

 

[superg33k]

Well if some parts of space are moving away faster than c (due to expansion so no relativity issue) I can understand why we still, and always will, receive CMB radiation. Kind of like always seeing someone falling into a black hole's event horizon.

However the Horizon Problem issue. Were some parts always moving away from each other faster than c (due to expansion again)? If this were the case then I could see how those parts have never been (or ever will be) in each others particle horizon but my understanding is that there is an accelerating expansion and I haven't heard that a requirement for the Horizon Problem is that parts of the universe have always been expanding greater than (or very lose to) c relative to each other. Is it the case?

Finally you said "The CMB is EVERYWHERE". Does this imply a finite universe, and hence a positive curvature?

Thanks for the post

 

[Drakkith]

However the Horizon Problem issue. Were some parts always moving away from each other faster than c (due to expansion again)? If this were the case then I could see how those parts have never been (or ever will be) in each others particle horizon but my understanding is that there is an accelerating expansion and I haven't heard that a requirement for the Horizon Problem is that parts of the universe have always been expanding greater than (or very lose to) c relative to each other. Is it the case?

I think it was simply that after inflation, right when the universe became transparent, different points in space were already so far apart that they will never be in each others horizons thanks to the accelerating expansion.

Finally you said "The CMB is EVERYWHERE". Does this imply a finite universe, and hence a positive curvature?

Thanks for the post

I don't believe so. Whether the universe is finite or not, the CMB was created, to the best of my knowledge, everywhere in the universe at the same time.

 

[Dotini]

Whether the universe is finite or not, the CMB was created, to the best of my knowledge, everywhere in the universe at the same time.

By definition, isn't CMB some remnant radiation that became separated from matter at a specific, early point in time?

Respectfully,
Steve

 

[superg33k]

By definition, isn't CMB some remnant radiation that became separated from matter at a specific, early point in time?

Respectfully,
Steve

Yeah CMB is the radiation from last scattering. Previous to last scattering the universe was a ionized plasma, but as it expanded radiation lost energy and the universe cooled so neutral atoms formed, so there was a lot less scattering and hence all the radiation was free to fly everywhere. CMB is all that radiation that hasn't been scattered since early hot ionized universe, i.e. the radiation from last scattering.

 

[superg33k]

I don't believe so. Whether the universe is finite or not, the CMB was created, to the best of my knowledge, everywhere in the universe at the same time.

I was assuming the universe has finite matter/radiation. Maybe I shouldn't make that assumption. If it wasn't I can see how an open universe could have CMB everywhere.

 

[Drakkith]

By definition, isn't CMB some remnant radiation that became separated from matter at a specific, early point in time?

Respectfully,
Steve

It is the radiation that was around when the universe became transparent.

 

[superg33k]

I think it was simply that after inflation, right when the universe became transparent, different points in space were already so far apart that they will never be in each others horizons thanks to the accelerating expansion.

I don't think this is right for a few reasons. Inflation is supposed to be a solution to the horizon problem, by your description it wouldn't be. Also from what I have read (from the few terrible online descriptions I can find) the parts of the CMB have never been in each others particle horizon. This makes sense as if they were previously in each others particle horizon, but only after such expansion weren't, then they could have establish equilibrium before expansion which would explain similar temperatures.

I think the horizon problem must be from the instant the particles were creates they have been moving relative to each other at speeds close to (or faster than) c (speed + expansion) so that they have never been in contact. Of course I'd be happier if someone could tell me this is right.

Also inflation solves the horizon problem by having 10^-32 seconds (or there about) after the universe was created when everything was in each others particle horizon (and therefore managed thermal equilibrium), then a massive inflation happens. From what I know of inflation (which is a little) it sounds like the biggest hack that I have heard of in physics. Its amazing how it managed to right, or at least make predictions consistent with fluctuations in the CMB.

 

[Drakkith]

I don't think this is right for a few reasons. Inflation is supposed to be a solution to the horizon problem, by your description it wouldn't be.

How so? Before inflation everything was within everything's horizon. Afterward the distances were so far apart that they lost "contact" with each other.

Also from what I have read (from the few terrible online descriptions I can find) the parts of the CMB have never been in each others particle horizon. This makes sense as if they were previously in each others particle horizon, but only after such expansion weren't, then they could have establish equilibrium before expansion which would explain similar temperatures.

Yes, that is exactly what inflation suggests.

I think the horizon problem must be from the instant the particles were creates they have been moving relative to each other at speeds close to (or faster than) c (speed + expansion) so that they have never been in contact. Of course I'd be happier if someone could tell me this is right.

The problem was that without something like inflation, we have no way to explain how the universe became so homogenous.

Also inflation solves the horizon problem by having 10^-32 seconds (or there about) after the universe was created when everything was in each others particle horizon (and therefore managed thermal equilibrium), then a massive inflation happens. From what I know of inflation (which is a little) it sounds like the biggest hack that I have heard of in physics. Its amazing how it managed to right, or at least make predictions consistent with fluctuations in the CMB.

It's not really that much of a hack. Many options were explored and eventually the one that added up the best was inflation.

 

[superg33k]

The problem was that without something like inflation, we have no way to explain how the universe became so homogenous.

Yes but why not?

From my understanding it's because "the particles were never within each others particle horizon". Then I ask again, why not? And I think the answer is "because ever since the big bang they have been moving apart close to, or faster than, c (velocity and expansion due to cosmological constant/dark matter)". Note that even though it has expansion, this is the big bang model without inflation.

One other point on inflation model. It's also my understanding that after inflation it was still about another 100 000 years before last scattering.

Do you agree with all this? Or is there a different reason particles have never been in each others particle horizon without inflation.

 

[Drakkith]

From my understanding it's because "the particles were never within each others particle horizon". Then I ask again, why not? And I think the answer is "because ever since the big bang they have been moving apart close to, or faster than, c (velocity and expansion due to cosmological constant/dark matter)". Note that even though it has expansion, this is the big bang model without inflation.

No, the answer is "because the universe is so vast that it is not possible for two areas greater than X distance from each other to be connected in any way."

Do you agree with all this? Or is there a different reason particles have never been in each others particle horizon without inflation.

Inflation SOLVES the horizon problem, it does not contribute to it. For example, if I look "east" and see a galaxy 10 billion light years away, and then look "west" and see another galaxy 10 billion light years away, those 2 galaxies have NEVER been in each others particle horizons because the distance between them is larger in light years than the age of the universe is in years. Since nothing can travel greater than c, then the overwhelming homogenous nature of the universe, such as the near uniformity of the CMB, should NOT be there.

 

[bapowell]

Yes but why not?

There is no reason to expect, a priori, that the big bang was a homogeneous event. You can simply say it was, but that's fine tuning. Inflation provides a dynamical explanation for the homogeneity and flatness of the universe.

 

[superg33k]

Inflation SOLVES the horizon problem.

I agree.

For example, if I look "east" and see a galaxy 10 billion light years away, and then look "west" and see another galaxy 10 billion light years away, those 2 galaxies have NEVER been in each others particle horizons because the distance between them is larger in light years than the age of the universe is in years. Since nothing can travel greater than c, then the overwhelming homogenous nature of the universe, such as the near uniformity of the CMB, should NOT be there.

This is basically the horizon problem statement. My issue is at the instant of the big bang those particles were infintisimally far away from each other. At that point were they within each others particle horizons? And if not, why not?

Just to make sure we are on the same page. Big bang model is a big bang happened, the universe expanded due to dark energy, at about 100 000 years (i think) last scattering happened, but expansion kept going, now everyhting is billions of light years apart. Inflation model is big bang happened, 10^-32s into it the universe inflated of a factor 10^70 (in a fraction of a second), about 100 000 years later last scattering happened, still the universe has dark energy and keeps expanding and now everything is billions of light years apart. Does this very briefly summerize them?

 

[superg33k]

There is no reason to expect, a priori, that the big bang was a homogeneous event. You can simply say it was, but that's fine tuning. Inflation provides a dynamical explanation for the homogeneity and flatness of the universe.

I agree with all this. My issue is in the horizon problem statement where it says parts of the universe have never been within each others particle horizons. Why were they not within each others particle horizons at the point of the big bang?

 

[Cosmo Novice]

I agree with all this. My issue is in the horizon problem statement where it says parts of the universe have never been within each others particle horizons. Why were they not within each others particle horizons at the point of the big bang?

They were - just after the Big Bang (I will not discuss t=0 only t>0) all particles were within each others event horizon in the early Universe.

All particles were initially in causal contact - this, coupled with inflation, provides a resolution to the inflation problem. At least this is how I understand it.

Your assertation that "the horizon problem statement where it says parts of the universe have never been within each others particle horizons" is false and seems to be causing you some confusion.

It is clear to note the distinction, of which I think you are aware, between expansion and inflation.

 

[bapowell]

I agree with all this. My issue is in the horizon problem statement where it says parts of the universe have never been within each others particle horizons. Why were they not within each others particle horizons at the point of the big bang?

Cosmologists avoid talking about the "point of the big bang". True, if all matter in the universe did indeed originate from a point of zero size, everything would already be trivially causally related and there would be no horizon problem. However, the standard big bang model applies only to the evolution of the universe after the big bang, in which initial data is encoded on a spacelike hypersurface after the big bang. In this case, there are inevitably points that lie outside each others' particle horizons. See the discussion of the horizon problem here : http://www.astro.ucla.edu/~wright/cosmo_03.htm" . In particular, examine the conformal spacetime diagram showing how points on the surface of last scattering have past lightcones that do not intersect on the hypersurface at t=0.

EDIT: Inflation solves the horizon problem by taking an initially tiny causal region and blowing it up to encompass at least the last scattering sphere.

 

[Cosmo Novice]

Cosmologists avoid talking about the "point of the big bang". True, if all matter in the universe did indeed originate from a point of zero size, everything would already be trivially causally related and there would be no horizon problem. However, the standard big bang model applies only to the evolution of the universe after the big bang, in which initial data is encoded on a spacelike hypersurface after the big bang. In this case, there are inevitably points that lie outside each others' particle horizons. See the discussion of the horizon problem here : http://www.astro.ucla.edu/~wright/cosmo_03.htm" . In particular, examine the conformal spacetime diagram showing how points on the surface of last scattering have past lightcones that do not intersect on the hypersurface at t=0.

EDIT: Inflation solves the horizon problem by taking an initially tiny causal region and blowing it up to encompass at least the last scattering sphere.

Thanks Bapowell,

The link will probably help me understand this as well. My assumption was that initially (shortly after t>0) all particles were in causal contact - thus inflation explains away blockbody radiation and spatial uniformity, however I may have to do a little more reading around this subject.

 

[superg33k]

Cosmologists avoid talking about the "point of the big bang".

Yeah, I should have been more clear. I meant just after. But NVM I'll be more clear below.

See the discussion of the horizon problem here : http://www.astro.ucla.edu/~wright/cosmo_03.htm" . In particular, examine the conformal spacetime diagram showing how points on the surface of last scattering have past lightcones that do not intersect on the hypersurface at t=0.

The diagram doesn't show the past light cones to t=0, it only shows a small part of the past light cone. Obviously all light cones intersect at t=0 (only the point), but since that is an infintisimal point and isn't explained without GUT's we don't know the physics of it, so t=0 isn't part of the discussion. My question is, do they have the light cones (in the big bang model without inflation) overlap at t=1s.

If light cones DON'T overlap at t=1s, then I conclude that they must be traveling apart at a speed close to, or faster than, the speed of light (by traveling apart I mean due to expansion and velocity). This is what I previously thought but have been told is wrong.

Alternatively, the light cones DO overlap, in which case this is exactly the solution inflation gives! Inflations solution is that they were in casual contact for 10^-32s (or about there) in which the universe manages thermal equilibrium, inflation then happens and lots of the universe is no longer in casual contact, 100 000 years happen until last scattering but still the approximate thermal equilibrium in that first 10^-32s allows the CMB to be similar throughout the universe.

So in the big bang theory without inflation, were different regions in casual contact at t=1s? If not, is it because they were traveling apart close to, or faster than, c?

 

[bapowell]

The diagram doesn't show the past light cones to t=0, it only shows a small part of the past light cone. Obviously all light cones intersect at t=0 (only the point), but since that is an infintisimal point and isn't explained without GUT's we don't know the physics of it, so t=0 isn't part of the discussion.

I see that you are assuming that the singularity was necessarily a point. This is not the conventional view of the big bang. Cosmological observations are instead consistent with a big bang that occurred uniformly everywhere at once (see https://www.physicsforums.com/showthread.php?t=506991" ) for more on this).

My question is, do they have the light cones (in the big bang model without inflation) overlap at t=1s.

The conformal spacetime diagram is just a way of illustrating the fact that the particle horizon at the time of last scattering subtended an angle of only 2 degrees on the last scattering surface. There simply wasn't enough time to equilibrate the entire last scattering surface at the time of decoupling.

If light cones DON'T overlap at t=1s, then I conclude that they must be traveling apart at a speed close to, or faster than, the speed of light (by traveling apart I mean due to expansion and velocity). This is what I previously thought but have been told is wrong.

Be careful here! Yes, inflationary expansion does cure this problem (it effectively moves the t=0 hypersurface earlier in time until all the light cones intersect -- and don't get hung up on the label 't=0', with the inclusion of inflation, it now coincides with the time that inflation ends). However, it is a common misconception that spacetime expanded faster than light speed during inflation -- in fact, points in space can separate at speeds surpassing that of light even in non-inflationary space times (the recession velocity depends on distance; the Hubble radius marks the separation at which two points recede from each other at a speed v=c, and therefore defines the scale of the causal region). The important difference during inflation is that space is expanding faster than the Hubble radius, so that points that are initially in causal contact can be pulled apart to regions of spacetime that would not otherwise be causally related in non-inflationary models.

 

[superg33k]

I see that you are assuming that the singularity was necessarily a point. This is not the conventional view of the big bang. Cosmological observations are instead consistent with a big bang that occurred uniformly everywhere at once (see https://www.physicsforums.com/showthread.php?t=506991" ) for more on this).

Everywhere was a point, but in a universe with infinite positive curvature! This also agree's with the FAQ you addressed (it doesn't mention the initial "size" but does mention infinite curvature which implies everywhere is a point).

 

[bapowell]

Everywhere was a point, but in a universe with infinite positive curvature! This also agree's with the FAQ you addressed (it doesn't mention the initial "size" but does mention infinite curvature which implies everywhere is a point).

I think you're confused: from the FAQ:

But even if time existed before the Big Bang, there is still another reason not to imagine the Big Bang as happening at one point in a preexisting empty space. Observations of the universe show a nearly complete lack of structure on very large scales, and the cosmic microwave background is also extremely uniform (with fractional temperature differences on the order of 10-5). For this reason, realistic cosmological models must be almost exactly homogeneous, meaning that no point in space has properties that differ very much from those of any other point. Therefore the best evidence is that the Big Bang happened uniformly, everywhere at once.

Keep in mind that, in the case of an infinite universe, it was always so. By assuming that the universe originated from a single point you are considering a special case.

 

[superg33k]

I'm becoming more certain that the answer must be that the big bang model requires space to be expanding faster (or very close to) c right after the big bang.

 

[bapowell]

I'm becoming more certain that the answer must be that the big bang model requires space to be expanding faster (or very close to) c right after the big bang.

So you didn't even read my reply about how it is not correct to consider space as expanding faster than c? It helps to listen What you are trying to say, is that inflation must have happened. In which case the whole of modern cosmology agrees with you.

 

[superg33k]

I don't think of the big bang as happening at one point in pre-existing space. I think of the big bang happening at one point which is all of space. Like an expanding balloon...deflated until its a point...

How can inifinite curvature describe anything with volume?

 

[bapowell]

I don't think of the big bang as happening at one point in pre-existing space. I think of the big bang happening at one point which is all of space. Like an expanding balloon...deflated until its a point...

How can inifinite curvature describe anything with volume?

It can't! Which is why the initial singularity is not a physically sensible solution. The balloon analogy works fine, but it doesn't start expanding from zero size -- it must have a small initial radius.

 

[superg33k]

in fact, points in space can separate at speeds surpassing that of light even in non-inflationary space times

So you didn't even read my reply about how it is not correct to consider space as expanding faster than c?

I read all your posts!

 

[superg33k]

It can't! Which is why the initial singularity is not a physically sensible solution. The balloon analogy works fine, but it doesn't start expanding from zero size -- it must have a small initial radius.

So in the big bang model without inflation, if it has a small initial radius, why is it not within each others particle horizon?

(BTW if I'm discussing anything but the big bang model without inflation I'll say. Its the horizon problem I is what I'm not getting, not the horizon solution :) )

 

[bapowell]

So in the big bang model without inflation, if it has a small initial radius, why is it not within each others particle horizon?

Because of the spacetime diagram I posted earlier. Given that we know when the CMB was generated, we can determine how far light could have traveled in that time. That distance, projected onto the last scattering sphere, subtends only a tiny fraction of the total angular expanse of the CMB sky. Therefore, there must have been causally disconnected regions of the universe at last scattering, and, by extension, just after the big bang.

 

[superg33k]

Therefore, there must have been causally disconnected regions of the universe at last scattering,

I agree.

and, by extension, just after the big bang.

How do you conclude this from the first statement?

 

[superg33k]

Just to keep everything on track, my question is:

Given that the universe initially had "a small initial radius." were particles that now casually disconnected regions of the CMB within each others particle horizon? And if not, is it because they were separating at a speed close to, or greater than, c? (separating by expansion)

 

[bapowell]

How do you conclude this from the first statement?

Nice catch. I forgot the important assumption: in a spacetime in which physical length scales, [itex]l_{\rm phys} \propto a(t)[/itex] (where [itex]a(t)[/itex] is the scale factor) expand (monotonically) at a slower rate than the Hubble radius, [itex]d_{H} \propto H^{-1}[/itex], i.e.
[tex]\frac{d}{dt}\left(\frac{d_{H}}{l_{\rm phys}}\right) > 0[/tex]
and if the physical separation between two points a and b at a time t* satisfies
[tex]l_{\rm phys}(t^*) > d_H(t^*)[/tex]
then [itex]l_{\rm phys}(t) > d_H(t)[/itex] for all [itex]t < t^*[/itex]. From
[tex]\frac{d}{dt}\left(\frac{d_{H}}{l_{\rm phys}}\right) = \frac{d}{dt} \left(\frac{1}{aH}\right) = -\frac{\ddot{a}}{\dot{a}^2} > 0[/tex]
we see that our assumption holds in all spacetimes for which [itex]\ddot{a}<0[/itex] -- non-inflationary spacetimes.

 

[superg33k]

Ok, the texts I have read didn't go into the horizon problem that mathsy but I think I got it. From what I gather you are saying that all points that are outside each others Hubble radius now have always been outside each others Hubble radius.

To apply this to the CMB I am going to assume that the 2 separate parts are outside each others Hubble radius which is why they are in casually disconnected regions of space. Thus they have always been outside each others Hubble radius. So they have been separating faster than c since the big bang?

 

[bapowell]

Ok, the texts I have read didn't go into the horizon problem that mathsy but I think I got it. From what I gather you are saying that all points that are outside each others Hubble radius now have always been outside each others Hubble radius.

Yes, for non-inflationary spacetimes, this is correct.

To apply this to the CMB I am going to assume that the 2 separate parts are outside each others Hubble radius which is why they are in casually disconnected regions of space. Thus they have always been outside each others Hubble radius. So they have been separating faster than c since the big bang?

Yes.

 

[superg33k]

Excellent. Thanks for going through this all with me. I'm happy to say the horizon problem makes sense. Additionally I never realized that non-infamitory models required a constant rate of expansion of the scale factor, which makes sense also.