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CAMB: Output the \psi and \phi
 
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gongbo zhao



Joined: 04 Jan 2005
Posts: 69
Affiliation: ICG, Portsmouth

PostPosted: March 21 2005  Reply with quote

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
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Antony Lewis



Joined: 23 Sep 2004
Posts: 1303
Affiliation: University of Sussex

PostPosted: March 21 2005  Reply with quote

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

k2Φ = κS2(δρ + 3Hq / k) / 2

The total matter perturbation (κS2δρ) and heat fluxe (κS2q) 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!
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