## Sachs-Wolfe and Doppler Transfer Functions

Use of Healpix, camb, CLASS, cosmomc, compilers, etc.
Posts: 7
Joined: January 05 2017
Affiliation: University of Alberta

### Sachs-Wolfe and Doppler Transfer Functions

I have been using your 'Camb' code to calculate transfer functions for my research. I am interested in calculation of $T_{SW}(k)$ and $T_{D}(k)$ where these are Sachs-Wolfe and Doppler terms as given in Eq. (7.3.58) DAMPT lectures on cosmology (http://www.damtp.cam.ac.uk/user/db275/Cosmology2015.pdf) so can you help me with that.

I also wanted to know the units of Camb code output velocity transfer functions $vel/k^2$ and if one multiplies $vel/k^2$ by $k^2$ then what will be the units of $vel$ Transfer functions 11, 12 13.

Antony Lewis
Posts: 1369
Joined: September 23 2004
Affiliation: University of Sussex
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### Re: Sachs-Wolfe and Doppler Transfer Functions

You can get individual terms for the sources by commenting appropriately the terms in output() in equations.f90. Doppler and ISW terms are already there (commented or not).

The transfer functions should be dimensionless (and normalized for unit initial superhorizon curvature perturbation).

Secondly, is there any way one can calculate the transfer function without the comoving perturbations $\mathcal{R}_k$ part as in Eq. 7.3.58 of Dampt lectures, $\Theta (k,\hat{n})= [T_{SW}(k)+i \cos(\theta)T_{D}(k)] \mathcal{R}_k$, as I just need $T_{D}$ and $T_{SW}$. You see, I calculate the power spectrum for the comoving perturbations using my own model (code) and I only need the $T_{SW}$ and $T_{D}$ part of the transfer functions.