B What is the Relation Between Jeans Mass and Fundamental Mode in Acoustic Waves?

[Discman]

I don't understand the difference between the Jeans Mass and the fundamental mode. Both are reaching till the horizon but according to me is the Jeans mass not oscillating. So what is the relation between a Jeans mass and the fundamental mode of the acoustic waves?

 

[Simon Bridge]

I don't understand the difference between the Jeans Mass and the fundamental mode.[

Without more context: they are completely different things.
Jeans mass is the critical mass for star formation from a diffuse particle cloud - it's a benchmark.
The fundamental mode is the longest wavelength acoustic (pressure wave) mode in the cloud.

what is the relation between a Jeans mass and the fundamental mode of the acoustic waves?

They do not need to be related. If the cloud is oscillating in some way, ie it may be pulsing at the fundamental, then parts of the cloud will have a higher mass (for that sub-volume) than others ... so it is possible that some parts of the cloud will exceed the Jeans mass (for that sub-volume) even if the entire cloud does not. However, the cloud will have a Jeans mass even if it is not pulsing.

 

[Chronos]

Irrelevant, the Jeans mass is merely a matter of fundamental classical physics. Acoustical waves are something we can measure. You need to clarify your question.

 

[bapowell]

I don't understand the difference between the Jeans Mass and the fundamental mode. Both are reaching till the horizon but according to me is the Jeans mass not oscillating. So what is the relation between a Jeans mass and the fundamental mode of the acoustic waves?

During radiation domination the Jeans length is of order the horizon size but still longer than the wavelength of the fundamental tone, so that all subhorizon modes oscillate as sound waves. See https://www.physicsforums.com/insights/poor-mans-cmb-primer-part-4-cosmic-acoustics/#refs

 

[Discman]

Thank you all, but bapowell catches my problem very well. Before I can react I have to study the interesting paper he quoted for me what will take some time.

 

[Discman]

After much reading I still don't understand your answer that there are already perturbations right after end of inflation. From this kind of figures they reappear late in the baryon-photon period. Do I make wrong conclusions from this and other figures?

A

 

[bapowell]

There are fluctuations existing on all scales at the end of inflation, marked by the bottom of the red "V" in the figure (the quantity 1/aH is a minimum at the end of inflation). However, what we see in the CMB are these fluctuations at recombination, after several scales have had the chance of re-entering the horizon. Upon re-entry, they begin to oscillate as sound waves: the fundamental tone has had time to compress just once by the time of recombination. Does this agree with your understanding?

 

[Discman]

Not totally. Why is the late re-entry always specified. Does this mean that all we see on the last scattering surface derives from the period between that re-entry and the sound-horizon.
What I also not understand is the correlation right after the end of inflation between the Hubble sphere which had during inflation a real (event)horizon and the then created particle horizon. According to me both are very different but on the figures they go on as a single line after inflation.

 

[bapowell]

Not totally. Why is the late re-entry always specified. Does this mean that all we see on the last scattering surface derives from the period between that re-entry and the sound-horizon.

We see everything from the present horizon all the way down to smaller scales well-within the sound-horizon at decoupling. However, only those modes with wavelengths on order of and smaller than the horizon at decoupling are oscillating (see Figure 4 in the article I referenced earlier).

What I also not understand is the correlation right after the end of inflation between the Hubble sphere which had during inflation a real (event)horizon and the then created particle horizon. According to me both are very different but on the figures they go on as a single line after inflation.

Can you reference a particular figure where you see this? Often in the literature, the Hubble sphere is taken to correspond to the event horizon, even though this identification is only true in de Sitter space.

 

[Discman]

I'm getting more and more confused. On all the figures of Wayne Hu I see oscillating sound waves originating right after end of inflation. Now you are telling me that they start oscillating after re-entering. Also on calculating the wavelength of the fundamental mode they take the full 380.000 years. From your explanation I understand that fluctuations start right after end of inflation while the perturbations are in a freezing mode behind the horizon. Please help me out of this trouble. I have the feeling that I take as observer a wrong position, have I to co-move with all the fluctuations?

 

[Discman]

Yes, the more I'm thinking about my last remark: as a co-mover I see it in the same way as Wayne Hu and as a steady observer on Earth I see according to bapowell? Right?

 

[bapowell]

I'm getting more and more confused. On all the figures of Wayne Hu I see oscillating sound waves originating right after end of inflation. Now you are telling me that they start oscillating after re-entering. Also on calculating the wavelength of the fundamental mode they take the full 380.000 years. From your explanation I understand that fluctuations start right after end of inflation while the perturbations are in a freezing mode behind the horizon. Please help me out of this trouble. I have the feeling that I take as observer a wrong position, have I to co-move with all the fluctuations?

I agree with Wayne and I don't believe I've contradicted him: one has fluctuations immediately after inflation, but only those within the horizon have had time to complete oscillations as sound waves. There are of course some modes within the horizon at the end of inflation, but those that are much larger are effectively frozen -- this is a simple causality argument. The horizon is not a hard boundary, beyond which all modes are completely frozen; indeed, the fundamental mode has a wavelength twice the horizon size and it has completed a half oscillation. The horizon can, however, be used as a quick way of separating the effectively frozen modes from the acoustic waves, and the temperature spectrum illustrates this fact (broad central peak corresponds to fundamental mode, with the correlation dying off at larger scales).

 

[Chronos]

No signal can propagate faster than light. Which means the consequences of physical events cannot be transmitted faster than c. That constrains physics in ways not always obvious.