SuperSampleCovariance.h File Reference

The class SuperSampleCovariance. More...

#include "Cosmology.h"

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Classes
class	cbl::cosmology::SuperSampleCovariance
	The class SuperSampleCovariance. More...

Namespaces
	cbl
	The global namespace of the CosmoBolognaLib
	cbl::cosmology
	The namespace of the functions and classes used for cosmological calculations

Detailed Description

The class SuperSampleCovariance.

This file defines the interface of the class SuperSampleCovariance, used to compute the \(S_{ij}\) matrix for the super-sample covariance.

Given two redshift bins, labelled as \(i\) and \(j\), \(S_{ij}\) is:

\( S_{ij} = \frac{1}{\Omega} \frac{1}{2\pi^2} \int {\rm d} k\,\, k^2 P(k) \frac{U_i(k)}{I_i} \frac{U_j(k)}{I_j}, \)

where \(\Omega\) is the survey area, \(P(k)\) is the power spectrum, and \(U_i(k)\) and \(I_i\) are expressed as:

\( U_i(k) = \int {\rm d} V_i \,\, W^2_i g(z_j) j_0(kr_j), \)

\( I_i = \int {\rm d} V_i \,\, W^2_i, \)

where \(V_i\) is the comoving volume within the \(i\)-th redshift bin, \(g\) is the growth factor, \(j_0\) the Bessel spherical function, and \(W_i\) is the window function.

Physical units are forced.

This code is a reimplementation of the Python code presented in Lacasa & Grain 2019. The original code can be found here: https://github.com/fabienlacasa/PySSC

Author

Giorgio Lesci

giorg.nosp@m.io.l.nosp@m.esci2.nosp@m.@uni.nosp@m.bo.it

Definition in file SuperSampleCovariance.h.