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### Tranfer function: Relative CDM Baryon Velocity

Posted: October 26 2015
Hi! I am new to CAMB and have been trying to use it to get the relative velocity between CDM and Baryons using the transfer function. I have a few questions and I would be really glad if someone could answer them:

1. What is the exact formula used for getting the 13th column of the transfer function data file? (Including the constants if any)

2. For some reason when I try to get the transfer function for a redshift >3000, the transfer function gives incomprehensible values. There is a lot of repetition in the rows and the first column (with k values) is of the order 10^(-18). So I am assuming it is some sort of numerical problem. Are there changes that I have to make in the params.ini file apart from the usual ones to get meaningful transfer function for high redshifts?

### Re: Tranfer function: Relative CDM Baryon Velocity

Posted: October 26 2015
The relative velocity transfer function T_{vb} is dimensionless. The file has T_{vb}/k^2 (where k/h is given in the first column) and k units are Mpc^{-1}.

The transfer functions are only intended to be output after recombination, and are not calculated before the time steps needed to get the CMB spectrum. What you are seeing may just be random unset values. It you set get_scalar_cls =F in the .ini file it - so it doesn't calculate the CMB spectra - it may work better as then the equations are just integrated directly to the requested redshift.

### Tranfer function: Relative CDM Baryon Velocity

Posted: October 27 2015
That worked! Thanks a ton. It is still unclear to me what is exactly meant by velocity transfer function? Is there a standard definition that I can look up somewhere (or some existing literature on the same)? From what I understand:
\begin{align} \textbf{v} &= - i \frac{a\textbf{k}}{k^2}\dot{\delta}(\textbf{k},a) \\ \implies \textbf{v} &= - i \frac{a\textbf{k}}{k^2}\dot{T}(\textbf{k},a)\delta_i(\textbf{k}) \end{align}
Thus may be CAMB gives out $$\dfrac{a\dot{T}(k,a)\sqrt[]{A_s}}{k}$$. Is that right?

PS: I am trying to obtain the velocity in real space in (km/s) using the transfer function and inverse-fourier transforming it. Thus I want to know what is exactly meant by the velocity transfer functions (columns 11, 12 and 13).

### Re: Tranfer function: Relative CDM Baryon Velocity

Posted: October 29 2015
Transfer functions are defined relative to unit initial curvature perturbation (they tell you how primordial modes transfer to late time, not the actual power at late times), so there's no factor of A_s, and it's the initial curvature perturbation not initial delta.