*** dlnP(k,z)/dz of Non-linear Matter Spectra from 3rd-order Perturbation Theory ***
April 6, 2012: E.Komatsu

There two programs:

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I. "generate_pkz3pt.f90"
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This program generates 2-dimensional arrays of non-linear matter power spectra, P(k,z), as a function of wavenumbers k [in units of h/Mpc] and redshifts z, using the 3rd-order perturbation theory:

P(k,z) = D^2(z)*P_11(k) + D^4(z)*[P_22(k)+2P_13(k)]

where P_11(k), P_22(k), and P_13(k) are pre-computed at z=30 and D(z) is the linear growth factor between z and z=30. We provide the data for these spectra in "wavenumber_pkd11_pkd22_pkd13_at_z=30.txt", which were generated by "compute_pk11pk22pk13", available also on CRL.

*** P(k) is in units of h^-3 Mpc^3, and k is in units of h Mpc^-1 ***
(This is the same as CAMB definition.)

The 3PT spectra were computed from the input linear power spectrum, "wmap5baosn_max_likelihood_matterpower.dat," which was generated using CAMB code for the maximum likelihood parameters given in Table I of Komatsu et al.(2008) [WMAP 5-year interpretation paper] with "WMAP5+BAO+SN". The input file for CAMB is also provided (wmap5baosn_max_likelihood_params.ini). NOTE THAT THIS POWER SPECTRUM IS COMPUTED AT Z=0.

Another power spectrum, evolved back to z=30, is provided as "wmap5baosn_max_likelihood_matterpower_at_z=30.dat".

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II. "compute_dlnpkdz3pt.f90"
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This program computes dlnpkdz in two different ways:

1. Reads in the arrays generated by "generate_pkz3pt" and calculates dlnP(k,z)/dz as a function of z for a given input value of k [h Mpc^-1], using a numerical differentiation with a spline interpolation. 

2. Computes dlnP(k,z)/dz directly from the 3PT formula:

dP(k,z)/dz = 2*D(z)*dD/dz*{ P_11(k) + 2*D^2(z)*[P_22(k)+2P_13(k)] }

and

dlnP(k,z)/dz = [1/P(k,z)]*dP(k,z)/dz


- To compile and use the program, edit Makefile and simply "make"
- It will generate executables called "generate_pkz3pt" and "compute_dlnpkdz3pt"
- Running "generate_pkz3pt" will generate 
  - redshift_wavenumber_pk3pt.txt

The format is
(1st) redshift
(2nd) wavenumber [h Mpc^-1]
(3nd) P(k,z) [h^-3 Mpc^3]

- Running "compute_dlnpkdz3pt" will generate 
  - redshift_dlnpkdz3ptnumerical_dlnpkdz3ptanalytical.txt

The format is
(1st) redshift
(2nd) dlnP(k,z)/dz from numerical differentiation
(3rd) dlnP(k,z)/dz from 3PT formula