Understanding Re-entry Perturbations After Inflation

[Discman]

Still I don't understand the meaning of the re-entry of perturbations in the horizon. OK, I understand the shortening of the Hubble radius opposite the length scales during inflation and the extension of the horizon after inflation. But what happened in the time after inflation till the re-entry? According to me fluctuations and oscillations were there all the time, most papers discuss the perturbations in the very early time. So I don't understand the special meaning of re-entry which happened much later, at least that is what I understand.

 

[Haelfix]

The point is those primordial fluctuations are frozen while they are on superhorizon scales. So after inflation ends, and the universe is in an unknown state with standard hot big bang evolution, it proceeds to evolve until it's Hubble horizon passes the re-entry scale. From that point forward, the intrinsic curvature of the spatial hypersurface defined with respect to the matter takes over the dynamics of the FRW dust solution and they are now allowed to participate in the dynamics.

This is very much what you want, it now gives you the desired 'initial' big bang conditions which provides the seed for the desired and observed structure formation (these 'are' the anisotropies we measure in the CMB). It 'sets' your initial conditions if you'd like to think of it like that.

 

[Discman]

I don't still understand what happens before the re-entry, especially in radiation period? The period of acoustic waves is always measured right from end of inflation. During inflation the Hubble horizon is indeed the point till where gravitation acts. But I understand from your answer that after inflation still the Hubble horizon is the point that acts as the re-entering while gravitation acts then till the real horizon after inflation, much further. So why unfreezes the perturbations after passing the Hubble horizon?

 

[Haelfix]

Sorry I don't quite follow your question. Are you asking why the scalar perturbations remain constant on superhorizon scales? There are as far as I know, only two ways to prove this, both found here (Start on page 40):

http://www.damtp.cam.ac.uk/user/db275/TEACHING/INFLATION/Lectures.pdf

After the modes re-enter the horizon, they behave as typical inhomogenieties in the CMB, and follow the same sorts of dynamics (again see those lectures for details, I mean there are entire courses on CMB physics)

 

[kimbyd]

Still I don't understand the meaning of the re-entry of perturbations in the horizon. OK, I understand the shortening of the Hubble radius opposite the length scales during inflation and the extension of the horizon after inflation. But what happened in the time after inflation till the re-entry? According to me fluctuations and oscillations were there all the time, most papers discuss the perturbations in the very early time. So I don't understand the special meaning of re-entry which happened much later, at least that is what I understand.

As long as the wavelength of the perturbation is longer than the horizon scale, it is impossible for information to travel from the peak to the trough of the perturbation, so the perturbation cannot oscillate (it isn't completely frozen: it does evolve, it's just that the speed of light limitations limit that change over time significantly).

Once the perturbation re-enters the horizon, the wave is able to oscillate again.

 

[Discman]

Dear kimbyd, thank you for your clarification. Still some questions

A perturbation longer than the horizon scale means that a part of it, let's say, the middle part, is lying sub horizontally. Doesn't that part also not oscillate?
Are there very small perturbations, so the latest generated ones, who after end inflation already very soon are entering the horizon. In fact what is the time scale for re-entering?

 

[kimbyd]

Dear kimbyd, thank you for your clarification. Still some questions

A perturbation longer than the horizon scale means that a part of it, let's say, the middle part, is lying sub horizontally. Doesn't that part also not oscillate?
Are there very small perturbations, so the latest generated ones, who after end inflation already very soon are entering the horizon. In fact what is the time scale for re-entering?

It will evolve over time (slowly), but it can't oscillate. Remember that these are pressure waves. Oscillation means the current high-pressure location becoming a low-pressure location, and vice versa for the current low-pressure location. That can't happen while the wave is super-horizon. The pressure locally will still change based upon local dynamics, but a full oscillation is impossible.