skypy.power_spectrum.growth_function_derivative

skypy.power_spectrum.growth_function_derivative(redshift, cosmology, gamma=0.5454545454545454)

First derivative of the growth function.

Function used to calculate D’(z), derivative of the growth function with respect to redshift as in [1] equation 16.

Parameters

redshift(nz,) array_like

Array of redshifts at which to evaluate the growth function.

cosmologyastropy.cosmology.Cosmology

Cosmology object providing methods for the evolution history of omega_matter and omega_lambda with redshift.

gammafloat

Growth index providing an efficient parametrization of the matter perturbations.

Returns

growth_function_derivative(nz,) array_like

The redshift scaling of the derivative of the growth function.

Notes

The first derivative of the growth function, \(D(z)\), with respect to redshift reads

\[D'(z) = - \frac{D(z) f(z)}{1 + z} \;.\]

With \(f(z)\) the growth factor.

References

1

5. 22. Linder, Phys. Rev. D 72, 043529 (2005)

Examples

This example returns the first derivative of the growth function for a given array of redshifts and cosmology:

>>> import numpy as np
>>> from scipy import integrate
>>> from astropy.cosmology import FlatLambdaCDM
>>> cosmology = FlatLambdaCDM(H0=67.04, Om0=0.3183, Ob0=0.047745)
>>> growth_function_derivative(0, cosmology)
-0.42360048051025856