Temperature Anisotropies !

 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. [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
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

 Posts: 1364
 Joined: September 23 2004
 Affiliation: University of Sussex
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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 [tex]C_l[/tex] 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 [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.
M.

 Posts: 1364
 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).