## CAMB: Output the \psi and \phi

Use of Healpix, camb, CLASS, cosmomc, compilers, etc.
gongbo zhao
Posts: 69
Joined: January 04 2005
Affiliation: ICG, Portsmouth
Contact:

### CAMB: Output the \\psi and \\phi

Dear all:
I want to get the \psi and \phi which are the potentials of Newtonian Gauge from CAMB. How can I do that ? Thanks in advance.

Cheers,
Gongbo Zhao

Antony Lewis
Posts: 1413
Joined: September 23 2004
Affiliation: University of Sussex
Contact:

### Re: CAMB: Output the psi and phi

Equations relating \Psi and \Phi to the synchronous gauge quantities used by CAMB are given in e.g. Eqs. A1,A2,etc of astro-ph/0212248. Usually it is easiest to use the Poisson equation

$k^2\Phi = \kappa S^2(\delta\rho + 3Hq/k)/2$

The total matter perturbation ($\kappa S^2\delta\rho$) and heat fluxe (\kappa\S^2\q) are called dgrho and dgq in CAMB's equations.f90. You could write them out in the fderivs or output routine.

Note however that the result for \Phi is numerically unstable on large scales, so if you require an accurate result on large scales (and an analytical one won't do) you may have to evolve the \Phi equation separately. (The early time series solution for \Psi is given in the notes).

Note also that I have seen every possible different sign convention for both $\Psi$ and $\Phi$!