CosmoCoffee

gongbo zhao · Joined: 04 Jan 2005 Posts: 47 Affiliation: ICG, Portsmouth

Dear all:
I want to get the

ψ

and

φ

which are the potentials of Newtonian Gauge from CAMB. How can I do that ? Thanks in advance.

Cheers,
Gongbo Zhao

Antony Lewis · Posted: March 21 2005

Equations relating

Ψ

and

Φ

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 Φ = κ S 2 (δρ + 3 H q / k) / 2

The total matter perturbation (

κ S 2 δρ

) and heat fluxe (

κ

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

Φ

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

Φ

equation separately. (The early time series solution for

Ψ

is given in the notes).

Note also that I have seen every possible different sign convention for both

Ψ

and

Φ

!