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### Angular power spectra of convergence using CAMB

Posted: **October 02 2020**

by **Ema SAE**

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.

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

Posted: **October 03 2020**

by **Antony Lewis**

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).

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

Posted: **October 04 2020**

by **Ema SAE**

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.

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

Posted: **October 04 2020**

by **Antony Lewis**

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.

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

Posted: **October 08 2020**

by **Ema SAE**

Hi,

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

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

Posted: **October 17 2020**

by **Ema SAE**

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]

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

Posted: **October 17 2020**

by **Antony Lewis**

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

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

Posted: **October 18 2020**

by **Ema SAE**

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?