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CAMB: Freeze growth in C_l's
Posted: February 21 2022
by Stefano Camera
Is there a simple way to freeze the growth of structures when computing harmonic-space power spectra for number count fluctuations with pyCAMB? In other words, the standard output is
[math]C^{ij}_\ell=\dfrac2\pi\int\mathrm{d}k\;\varDelta^i_\ell(k)\,\varDelta^j_\ell(k)\,P_\mathrm{lin}(k)\;,
with (omitting everything but density for simplicity)
[math]\varDelta^i_\ell(k)=\int\mathrm{d}z\;n^i(z)\,b(z)\,D(z)\,j_\ell[k\,r(z)]\;.
Instead, what I'd like is
[math]\varDelta^i_\ell(k)=\int\mathrm{d}z\;n^i(z)\,b(z)\,D(z=0)\,j_\ell[k\,r(z)]\;.
Re: CAMB: Freeze growth in C_l's
Posted: February 22 2022
by Antony Lewis
No (it's not well defined in general, e.g. with massive neutrinos growth is k dependent).
Re: CAMB: Freeze growth in C_l's
Posted: February 22 2022
by Stefano Camera
Thanks Antony. Yes, you're right, what I wrote doesn't hold in general, but it's the same as saying
[math]\varDelta_\ell^i(k)=\int\mathrm{d}z\;n^i(z)\,b(k,z)\,D(k,z=0)\,j_\ell[k\,r(z)]\;,
where I also allowed for scale-dependence in the bias.