sigma_r¶

Compute anisotropy dispersion sigma(R,z)

sigma(R,z) is the variance of cosmic density fluctuations on scales down to 8 Mpc/h.

In Fourier space is given by sigma(R,z) = int_0^infty W^2(k R) k^2 P(k,z) / (2 pi)^2 dk

The P(k,z) used could in general be linear or non-linear, but usually when people say sigma they mean the non-linear variant.

Assumptions¶

minimal assumptions; sigma computed directly from P(k,z)

Name	Type	Default	Description
zmin	real		Minimum redshift to generate values for
zmax	real		Maximum redshift to generate values for
dz	real		Output redshift sample spacing
rmin	real		Minimum scale R in Mpc/h to generate values for
rmax	real		Maximum scale R in Mpc/h to generate values for
dr	real		Scale R spacing
matter_power	str	matter_power_lin	Name of section to get P(k,z) from, e.g. matter_power_lin, matter_power_nl
crop_klim	bool	True	Crops the klimits of the sigma integral to max(0.01/R, kmin), min(100/R, kmax)

Section	Name	Type	Description
matter_power_lin	k_h	real 1d	Sample values of linear spectrum in Mpc/h. Section name specified by parameter in ini file.
	z	real 1d	Redshift of linear spectrum samples. Section name specified by parameter in ini file.
	P_k	real 2d	Linear spectrum in (Mpc/h)^{-3}. Section name specified by parameter in ini file.

Output values¶
Section	Name	Type	Description
sigmar	R	real 1d	Scale R of output in Mpc/h
	z	real 1d	Redshift of output
	sigma2	real 2d	Variance sigma^2(R,z)