Temperature Anisotropies !

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

Temperature Anisotropies !

Post by Muhammad Junaid » March 28 2017

Hi everyone,

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

Thanks in Advance!!

M Junaid

Antony Lewis
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Joined: September 23 2004
Affiliation: University of Sussex
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Re: Temperature Anisotropies !

Post by Antony Lewis » March 28 2017

Are you sure you don't want to calculate the C 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).

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

Temperature Anisotropies !

Post by Muhammad Junaid » March 28 2017

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

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

Temperature Anisotropies !

Post by Muhammad Junaid » March 30 2017

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

M.

Antony Lewis
Posts: 1352
Joined: September 23 2004
Affiliation: University of Sussex
Contact:

Re: Temperature Anisotropies !

Post by Antony Lewis » March 30 2017

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).

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