## Angular power spectra of convergence using CAMB

Use of Cobaya. camb, CLASS, cosmomc, compilers, etc.
Ema SAE
Posts: 5
Joined: October 02 2020
Affiliation: University of Sydney

### Angular power spectra of convergence using CAMB

Hi, I'm a new CAMB user. Currently, I'm trying to calculate the angular power spectra of convergence using Limber's approximation. I have already calculated the matter power spectrum using CAMB, but now I'm a bit confused when trying to calculate convergence angular power spectra using CAMB.
So, I have seen that from the 32 no. cell of this example notebook CAMB Demo, one can calculate the matter power spectra for Weyl potential and from the cell no. 33 one can calculate the convergence angular power spectra and plot it in cell no. 34. Did the authors use the Limber approximation here to calculate convergence angular power spectra? If so, where did they integrate the lensing efficiency function here? These are really confusing to me, hope I will get some proper answers from here. Thanks.

Antony Lewis
Posts: 1807
Joined: September 23 2004
Affiliation: University of Sussex
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### Re: Angular power spectra of convergence using CAMB

The line marked "limber" in 34 used the Limber approximation. Box 33 puts in the geometric factors (for CMB lensing the source is approximated to good accuracy as a single source plane at comoving distance chistar, so no integration over source redshift here).

Ema SAE
Posts: 5
Joined: October 02 2020
Affiliation: University of Sydney

### Re: Angular power spectra of convergence using CAMB

Hi,
Thanks for your reply. Sorry - still now things are not clear to me. Does the plot in box 34 show the angular power spectra of convergence from Limber approximation? If so, the plot looks good, but when I tried to change the matter power interpolator from Weyl potential to CDM + baryon density then the plot looks like this (https://drive.google.com/file/d/11EmKuRnceHPUBZ1nCmOfLiM4sy6ovVq7/view?usp=sharing). But the value of angular power spectra from Limber approximations in this plot should not be so high, right? It should be in the order of 10^-5 or something like that. I hope your answers will be helpful for me to get a clear idea. Thanks in advance.
NB: I'm just interested to calculate the convergence angular power spectra theoretically.

Antony Lewis
Posts: 1807
Joined: September 23 2004
Affiliation: University of Sussex
Contact:

### Re: Angular power spectra of convergence using CAMB

You should calculate it from the Weyl potential, it's that which actually causes light bending and hence is most appropriate for calculating convergence (Weyl potential is equal to Phi+Psi). If you want to relate to matter, you have to use the Poisson equation, but you need to include the other factors in there consistently.

Ema SAE
Posts: 5
Joined: October 02 2020
Affiliation: University of Sydney

### Re: Angular power spectra of convergence using CAMB

Hi,
Thank you so much. I have tried with Weyl potential and it worked for me.

Ema SAE
Posts: 5
Joined: October 02 2020
Affiliation: University of Sydney

### Re: Angular power spectra of convergence using CAMB

Hi,
Is there any way to calculate 'cl_camb', which means the 'CAMB hybrid' data as a function of redshifts? Please see cell number 34 in CAMB notebook [https://camb.readthedocs.io/en/latest/CAMBdemo.html]

Antony Lewis
Posts: 1807
Joined: September 23 2004
Affiliation: University of Sussex
Contact:

### Re: Angular power spectra of convergence using CAMB

Sorry, I don't understand what you mean. In that box cl_camb is a CMB lensing potential power spectrum.

Ema SAE
Posts: 5
Joined: October 02 2020
Affiliation: University of Sydney

### Re: Angular power spectra of convergence using CAMB

I'm talking about the power spectra plot in cell no 34 in the CAMB notebook, there is a line for CAMB hybrid here that you have calculated from 'cl_camb'. I'm thinking that - is there any way to calculate this 'cl_camb' at other redshifts, for example - at 0.5 redshift?