speed of sound term

[xzackli]

From @jmsull,

When I look at the MB expression (eqn 67) for the baryon velocity, there is a speed of sound term that is proportional to delta_b that is missing in Callin/Dodelson (and Bolt). Shouldn't we have that?

I should get to the bottom of this...

[jmsull]

Tangentially related - this paper argues that CLASS and CAMB are both wrong in the baryon EoMs (and that MB is not consistent with itself between eqn 30 and 67). I have not looked through the details but the changes presented in the conclusion would seem to take next to no effort to implement (but haven't thought about cost).

[jmsull]

And coming back to the original question, the sound speed term is just dropped in Dodelson because he reuses the cdm eqns (in which the first moment of boltzmann has (p/E)^2 terms dropped) but with the additional photon coupling term. So the assumption of doing this is that baryons are cold and have no sound speed just like cdm. The reason given for keeping it in MB is that even though cs_b << 1, at high enough k the c_s^{2} k^{2} \delta_{b} term is still important (baryons are not totally cold).

[xzackli]

We should insert the c_s^2 k^2 \delta_{b} term into the current hierarchy!. This is a really nice catch! I'll add a c_s function in ionization.jl. We can get the matter and radiation temperature out of both RECFAST and Peebles, which I hope to finish by the end of this week (it's slightly involved as RECFAST internally calculates a background, and I need to adapt that to our bg).

The Pookkillath paper is a lot of fun, and we should definitely make those photon/baryon Boltzmann equations an option. It looks to be very subdominant, so I think we can safely put that off for some time.

[xzackli]

Should close this when we finish adding it in.

[jmsull]

I added a spline for this to IonizationHistory in #44, cs2b(x) seems to match roughly with CLASS at intermediate times (1st attached), but something is happening at high redshift, and we also do not have reionization (2nd attached is an internal comparison of CLASS with default reionization and with it switched off, vertical line is at redshift 8). I will open a new issue for reionization.

[jmsull]

Both of these issues are qualitatively fixed in 43954ae - the high and low redshift disagreement in csb^2 was due to the previous expression (which I got out of MB) neglecting time evolution of mean mu, which is relevant early on and during reionization. Separately, this now agrees with CLASS with reionization turned on after including change in baryon temp due to reionization (#51).

There is still some offset and numerical wiggling going on around the transition to reionization at the level of 2% - warrants further checking but I think this is ok for now(?).

Quick plot attached, bottom is csb2_Bolt/csb2_CLASS. nr is the no-reionization model.