## Temperature Anisotropies !

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

### Temperature Anisotropies !

Hi everyone,

I just have one simple question question, I want to calculate the temperature anisotropies as a function of wave number i.e. $\Delta T(k)/T$ using the list of transfer functions output from the camb code. I just want to use my own initial power spectrum $P_\zeta(k)$ of initial perturbations(comoving curvature perturbations) to calculate $\langle \Delta T^2(k)/T^2 \rangle = \Delta_i^2(k) P_\zeta(k)$. Where $\Delta_i(k)$ would be some combination of transfer functions of the camb code. So, what precise combinations of transfer functions do I need here as $\Delta_i$'s?

M Junaid

Antony Lewis
Posts: 1363
Joined: September 23 2004
Affiliation: University of Sussex
Contact:

### Re: Temperature Anisotropies !

Are you sure you don't want to calculate the C_\ell power spectrum? That's easily done by modifying CAMB's power_tilt.f90 to use your own initial power spectrum (and increasing accuracy settings if needed).

Posts: 7
Joined: January 05 2017
Affiliation: University of Alberta

### Temperature Anisotropies !

No we are working out some moments in momentum space so we don't need $C_l$ or any angular part.

Posts: 7
Joined: January 05 2017
Affiliation: University of Alberta

### Temperature Anisotropies !

My hunch is that the temperature anisotropy is to leading order equal to $\Delta T/T \approx \frac{1}{4} \hat{\Delta}_\gamma+ 2\Phi$, where $\Phi$ is Weyl potential. While, you have said in your notes that power spectrum of Weyl potential is $P_\Phi=T_\Phi(k) P_\zeta(k)$ where $\zeta$ is primordial perturbations. Is the same true for other power spectra as $\Delta_\gamma^2 = \hat{\Delta}_\gamma^2 P_\zeta(k)$. So the transfer function output from the camb code are $\hat{\Delta}_\gamma^2$ that don't include the primordial power spectrum $P_\zeta(k)$. Please correct me if I am wrong!

M.

Antony Lewis
Posts: 1363
Joined: September 23 2004
Affiliation: University of Sussex
Contact:

### Re: Temperature Anisotropies !

Transfer function outputs are not squared (and indeed not scaled by the primordial power). The temperature sources are quite complicated in general (calculated in output routine of equations.f90).