CAMB Matter Power to Newtonian gauge

[Thomas Levi]

For various reasons I need the matter power spectrum computed in Newtonian gauge (as I understand it, CAMB default computes in synchronous) at various redshifts. Does anyone know where in the code I can go to modify the computation? and possibly even the necessary mods?

[Antony Lewis]

See outtransf in equations.f90.

For cdm newtonian gauge perturbation you want

Code: Select all

clxc - 3*adotoa*sigma/k

(not all variables may be defined in this subroutine by default).

This is for unbiased unevolving tracer of cdm, c.f 1105.5292

[Thomas Levi]

Hi Antony,

That's the CDM transfer function, which isn't quite what I need. I'm trying to generate a realization of (Newtonian gauge) matter perturbations at the end of inflation, which I can then evolve forward to any redshift using the transfer function you mention (which I already converted to Newtonian gauge). I want to be able to generate multiple realizations for a given set of parameters, just as I can say use the [tex]C_l[/tex]s to generate a realization of [tex]a_{lm}[/tex]s.

I thought the appropriate quantity was the normalized matter power spectrum that CAMB outputs in its own file (in synchronous gauge), yes? if so, that's what I need to convert over. If not, what quantity can I use?

[Antony Lewis]

The transfer functions in CAMB are all synchronous gauge.

So not sure why you want it, but you could calculate the power spectrum of the super-Hubble newtonian gauge matter pertubrations directly from the power spectrum of the curvature perturbation (they'll just be proportional for modes well outside the horizon).

[Thomas Levi]

Basically I'm attempting to generate many realizations of the matter fluctuations due to the usual perturbations to compare to a non-Gaussian signal in lensing and galaxy counts that I have, so I can calculate things like Fisher matrices and the like. Since all of my previous lensing etc. computations use the Newtonian gauge, I need the realizations in that gauge as well. Does that help?


The curvature perturbation itself would likely suffice in Newtonian gauge, I could then calculate a realization of it and use the CDM + baryon transfer functions to get a realization of the matter distribution at a given redshift. Yes?


Yup, I know they are all in synchronous gauge, I coded the change to Newtonian gauge for the transfer functions themselves (and the Newtonian potential) a while back. Thanks though.

[Antony Lewis]

You should just calculate the power spectrum normally at the later redshift and make a realisation of that. What I originally suggested will give you the Newtonian gauge cdm linear power spectrum at your redshift of choice.

For lenisng you normally want synchronous gauge density perturbations because they're what appear in the Poisson equation for the potential. (not that it really matters for current sub-hubble observations)

[Thomas Levi]

Hi Antony,

Apologies for the confusion, but I'm not sure how. The transfer functions are independent of any initial conditions, and it's precisely a realization of those (which I can then propagate forward with the transfer functions) that I'm trying to get at, i.e. I want to constrain [tex] \delta(k) [/tex] and for that I need the matter power spectrum, right?