## CAMB-- Power spectrum factorization

Use of Cobaya. camb, CLASS, cosmomc, compilers, etc.
Nicolò Dalmasso
Posts: 5
Joined: February 19 2021
Affiliation: University of Turin

### CAMB-- Power spectrum factorization

Hello everybody,

I've a question regarding the factorization that CAMB use when is calculating the angular power spectrum (Cl).
What is the correct factorization with these "counts" set to "True"?

pars.SourceTerms.counts_density = True
pars.SourceTerms.counts_redshift = True
pars.SourceTerms.counts_lensing = True

For instance I know that the correct factorization for the case:

pars.SourceTerms.counts_density = True
pars.SourceTerms.counts_redshift = True
pars.SourceTerms.counts_lensing = False

is: Cl_CAMB[i,j]= (bi*bj)*(Cl_bb[i,j]) + (fi*fj)*(Cl_ff[i,j]) + (bi*fj + bj*fi)*(Cl_bf[i,j])

Antony Lewis
Posts: 1724
Joined: September 23 2004
Affiliation: University of Sussex
Contact:

### Re: CAMB-- Power spectrum factorization

CAMB doesn't calculate it using a factorization, it calculates a single source term include the various sources adding them, then calculate the C_l. counts_lensing includes magnification bias.

Nicolò Dalmasso
Posts: 5
Joined: February 19 2021
Affiliation: University of Turin

### Re: CAMB-- Power spectrum factorization

Yes, that is for sure, but my question was:

If I want to do the reverse and reobtain the value that CAMB gives me in this particular set of parameters what is the correct factorization to use?

Like I said I know that the correct factorization to reobtain the (density,redshift) case is the one that I written before, but I'm not sure about the (density,redshift,lensing) case.

Antony Lewis
Posts: 1724
Joined: September 23 2004
Affiliation: University of Sussex
Contact:

### Re: CAMB-- Power spectrum factorization

You'd just have to add the auto and all the crosses for the magnification bias term.

Nicolò Dalmasso
Posts: 5
Joined: February 19 2021
Affiliation: University of Turin

### Re: CAMB-- Power spectrum factorization

Thanks!

I've tried to use:

Cl_CAMB[i,j]= (bi*bj)*(Cl_bb[i,j]) + (fi*fj)*(Cl_ff[i,j]) + (si*sj)*(Cl_ss[i,j]) + (bi*fj + bj*fi)*(Cl_bf[i,j]) + (bi*sj + bj*si)*(Cl_bs[i,j]) + (fi*sj + fj*si)*(Cl_sf[i,j])

but it seems to be incorrect and does not recreate the one calculated by CAMB, so I do not know what term I'm missing.