wl_spectra_ppf¶
Compute weak lensing C_ell from P(k,z) and MG D(k,z) with the Limber integral
File |
shear/spectra-ppf/interface.so |
Attribution |
CosmoSIS team |
Matt Becker |
|
URL |
DEPRECATED: You should use the module cosmosis-standard-library/structure/projection_ppf/project_2d_ppf.py instead. This variant of the wl_spectra module includes modified gravity via the phenomenological D(k,z) which modifies the lensing kernel. Compare equations 33 and 34 of http://arxiv.org/pdf/1109.4583v3.pdf Intrinsic alignments under modified gravity are not correctly supported; please use intrinsic_alignments=F
The Limber approximation integrates a 3D power spectrum over the radial direction to get a 2D angular power spectrum. It is an approximation which is only valid on smaller scales. \(C_\ell = A \int_0^{\chi_1} W_1(\chi) W_2(\chi) P(k=l/\chi, z(\chi)) / \chi^2 d\chi\)
The full integral must integrate over k(ell) also. For weak lensing, the power spectrum is the matter power spectrum and the two kernel functions W depend on the redshift bins being used and the geometry. Parts of this code and the underlying implementation of limber are based on cosmocalc: https://bitbucket.org/beckermr/cosmocalc-public
Assumptions¶
The Limber integral is valid on the scales in question
Setup Parameters¶
Name |
Type |
Default |
Description |
|---|---|---|---|
n_ell |
int |
Number of log-spaced ell values to compute |
|
ell_min |
real |
Minimum ell value to compute |
|
ell_max |
real |
Maximum ell value to compute |
Input values¶
Section |
Name |
Type |
Default |
Description |
|---|---|---|---|---|
modified_gravity |
k_h |
real 1d |
Wavenumber k/h sample points for D(k,z) |
|
z |
real 1d |
Redshift sample points for D(k,z) |
||
D |
real 2d |
D(k,z) values at sample points |
||
cosmological_parameters |
omega_m |
real |
Density fraction of all matter; used in the prefactor |
|
h0 |
real |
Hubble factor H0 / 100 km/s/Mpc. |
||
distances |
z |
real 1d |
Redshift values of distance samples |
|
d_m |
real 1d |
Comoving distnace to redshift values in units of Mpc (no factor h) |
||
matter_power_nl |
z |
real 1d |
Redshift values of P(k,z) samples |
|
k_h |
real 1d |
Wavenumber k values of P(k,z) samples in units of Mpc/h |
||
P_k |
real 2d |
Non-linear matter power spectrum at samples in (Mpc/h)^{-3} |
||
wl_number_density |
nbin |
int |
Number of redshift bins |
|
z |
real 1d |
Redshift values of n(z) samples |
||
bin_{i} |
real 1d |
Bin n(z) values. Need not be normalized. bin_1, bin_2, bin_3, …. |
Output values¶
Section |
Name |
Type |
Description |
|---|---|---|---|
shear_cl |
ell |
int 1d |
Sample ell values for output C_ell |
nbin |
int |
Number of redshift bins used |
|
bin_{i}_{j} |
real 1d |
C_ell (no l(l+1) factor) for (auto-correlation) bin i and j. Only stores j<=i. |