Documented cosmology module. More...

#include "header.h"

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Functions
int	Cosmology_init (struct Cosmology Cx, double pk_kmax, double pk_zmax, int nlines, int line_type, size_t npoints_interp, double M_min, long mode_mf)
	Allocate memory and initialize the cosmology structure, which includes the CLASS cosmology structure and line strucrure. More...

int	Cosmology_free (struct Cosmology *Cx)
	Free the memory allocated to cosmology structure. More...

int	CL_Cosmology_initilize (struct Cosmology *Cx, double pk_kmax, double pk_zmax)
	Allocate memory and initialize the CLASS cosmology structure. More...

int	CL_Cosmology_free (struct Cosmology *Cx)
	Free the memory allocated to CLASS cosmology structure. More...

struct PS_xtr *	PS_xtrapol_init (struct Cosmology *Cx)
	Call CLASS and build a 2d interpolator for Plin(k,z), which will be used when building an extrapolator for P(k,z) beyond a given kmax computed by CLASS. More...

int	PS_xtrapol_free (struct PS_xtr *PS_xtrapol)
	frees the interpolation elements for P_m spline More...

double	PS (struct Cosmology *Cx, double k, double z)
	Evaluate the extrapolation for matter power spectrum beyond what is calculated by CLASS, same expansion as that used in CORE cosmology librrary (see arXiv:1812.05995) If requested k-value was beyond what is calculated by CLASS, this function extrapolates. More...

double	PS_class (struct Cosmology *Cx, double k, double z, long mode)
	Call CLASS-V3.1 functions to compute the cdm+b pk (in Mpc**3) for a given k (in 1/Mpc) and z In LIM_FISHER code, we always include massive neutrinos. More...

double	Pk_dlnPk_HV (struct Cosmology *Cx, double k, double z, int mode)
	Read in the linear power spectrum, used to set the initial conditions of Hidden-Valley sims. More...

double	transfer (struct Cosmology *Cx, double k, double z, int mode)
	call CLASS-V3.1 to compute transfer function for different species depending on the switch "mode" mode can be set to cdm, baryons or total matter transfer function. More...

double	growth_D (struct Cosmology *Cx, double k, double z)
	Compute the growth factor D(k,z) for a general case where it can be scale-dependant The scale-dep growth is calculated by taking the ratio of the transfer function at redshift z and zero. More...

double	growth_f (struct Cosmology *Cx, double k, double z)
	Compute the growth factor D(k,z) by taking the ratio of the transfer function at redshift z and zero. More...

double	scale_indep_growth_D (struct Cosmology *Cx, double z)
	Compute the growth factor D(k,z) which is scale-indep valid when neutrinos are massless The scale-dep growth is calculated by taking the ratio of the transfer function at redshift z and zero. More...

double	scale_indep_growth_f (struct Cosmology *Cx, double z)
	Compute the scale-independent growth rate f(z) which is scale-indep valid when neutrinos are massless. More...

double	Hubble (struct Cosmology *Cx, double z)
	Compute the the hubble rate (exactly the quantity defined by CLASS as index_bg_H in the background module). More...

double	angular_distance (struct Cosmology *Cx, double z)
	Compute the angular diameter distance (exactly the quantity defined by CLASS as ba.index_bg_ang_distance in the background module). More...

double	comoving_radial_distance (struct Cosmology *Cx, double z)
	Compute the comoving radial distance More...

double	sig_sq_integrand (double x, void *par)
	The integrand function passed to qags integrator to compute the variance of the smoothed matter density. More...

double	sig_sq (struct Cosmology *Cx, double z, double R)
	Compute variance of smoothed matter density fluctuations. More...

double	der_lnsig_sq (struct Cosmology *Cx, double z, double R)
	Compute the logarithmic derivative of the variance of smoothed matter density fluctuations w.r.t. More...

double	sigma0_sq_integrand (double x, void *par)
	The integrand function passed to qags integrator to compute the variance of the unsmoothed matter density. More...

double	sigma0_sq (struct Cosmology *Cx, double z, double kmax)
	Compute variance of unsmoothed matter density fluctuations. More...

double	rhoc (struct Cosmology *Cx, double z)
	Compute the critical density in unit of M_sun/Mpc^3. More...

double	R_scale (struct Cosmology *Cx, double h_mass)
	Compute the Lagrangian radius of halos in unit of Mpc , fixing z=0. More...

double	R_scale_wrong (struct Cosmology *Cx, double z, double h_mass)
	Compute the Lagrangian radius of halos in unit of Mpc at z. More...

double	R_vir (struct Cosmology *Cx, double M)
	Compute the comoving virial radius of halos in unit of Mpc, which is defined as the radius at which the average density within this radius is Delta X rho_c. More...

double	concentration_cdm (double M, double z)
	Compute the cold dark matter concentration-mass relation. More...

double	nfw_profile (struct Cosmology *Cx, double k, double M, double z)
	Compute the NFW halo profile in Fourier space, given by Eq. More...

double	window_rth (double k, double R)
	Fourier transform of top-hat window in real space. More...

double	window_kth (double k, double R)
	Top-hat window in Fourier space. More...

double	window_g (double k, double R)
	Gaussian window. More...

double	derR_window_rth (double k, double R)
	Derivative w.r.t. More...

double	derR_logwindow_g (double k, double R)
	Derivative w.r.t smoothing scale of Gaussian window. More...

Detailed Description

Documented cosmology module.

Azadeh Moradinezhad Dizgah, November 4th 2021

The first routine of this module initalizes the Cosmology structure, which is the main building block of this entire code. This structure includes two sub-structures: the CLASS cosmology structure and line structure. Once the CLASS cosmology is initialized, various useful functions can be directly called from CLASS, example to compute matter power spectrum and transfer function, angular and comoving radii, growth factor and growth rate, variance of matter fluctuations and its derivative. Lastly, the module also includes various window functions and their derivatives.

In summary, the following functions can be called from other modules:

Cosmology_init() allocates memory to and initializes cosmology structure
Cosmology_free() frees the memory allocated to cosmology structure
CL_Cosmology_initilize() initializes the class cosmology structure
CL_Cosmology_free() frees the class cosmology structure
PS_xtrapol_init() initizalizes the interpolator for Pm(k,z)
PS_xtrapol_free() frees the interpolator for Pm(k,z)
PS() computes matter power spectrum calling class and extrapolating if k>kmax computed by class
PS_class() calls class to calculate
Pk_dlnPk_HV() reads in the mesaured Pm on HV simulation and interpolates
transfer() computes matter transfer function calling class function
growth_D() computes the scale-dep growth factor
growth_f() computes the scale-dep growth rate dlnD(k,a)/dlna
scale_indep_growth_D() computes the scale-indep growth factor using directly CLASS functions
scale_indep_growth_f() computes the scale-indep growth rate dlnD(k,a)/dlna using directly CLASS functions
Hubble() computes hubbble parameter using directly CLASS functions
angular_distance() computes angular diamtere distance using directly CLASS functions
comoving_radial_distance() computes radial distance using directly CLASS functions
sig_sq() computes variance of smoothed matter fluctuations
der_lnsig_sq() computes natural log derivative of the variance of smoothed matter fluctuations w.r.t. smoothing scale
sigma0_sq() computes variance of unsmoothed matter fluctuations
rhoc() computes the critical density of the universe
R_scale() computes the size of a spherical halo corresponding to a given mass at z=0
R_scale_wrong() computes the size of a spherical halo corresponding to a given mass at a given redshift
R_vir() computes the virial radius
concentration_cdm() computes the halo concentration
nfw profile() computes the nfw profile
window_rth() computes top-hat filter in real space
window_g() computes Gaussian window
window_kth() computes top-hat filter in Fourier space
derR_window_rth() computes derivative of top-hat filter in real space w.r.t. smoothing scale
derR_logwindow_g() computes derivative of top-hat filter in Fourier space w.r.t. smoothing scale

Function Documentation

◆ angular_distance()

double angular_distance	(	struct Cosmology *	Cx,
		double	z
	)

Compute the angular diameter distance (exactly the quantity defined by CLASS as ba.index_bg_ang_distance in the background module).

luminosity distance d_L = (1+z) d_M angular diameter distance d_A = d_M/(1+z) where d_M is the transverse comoving distance, which is equal to comoving distance for flat cosmology and has a dependance on curvature for non-flat cosmologies, as described in lines 849 - 851

Parameters

Cx	Input: pointer to Cosmology structure
z	Input: redshift to compute the spectrum

Returns: D_A

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◆ CL_Cosmology_free()

int CL_Cosmology_free ( struct Cosmology * Cx )

Free the memory allocated to CLASS cosmology structure.

Parameters

Cx	Input: pointer to Cosmology structure

Returns: the error status

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◆ CL_Cosmology_initilize()

int CL_Cosmology_initilize	(	struct Cosmology *	Cx,
		double	pk_kmax,
		double	pk_zmax
	)

Allocate memory and initialize the CLASS cosmology structure.

Parameters

Cx	Input: pointer to Cosmology structure
pk_kmax	Input: kmax for computation of matter power spectrum by CLASS
pk_zmax	Input: zmax for computation of matter power spectrum by CLASS

Returns: the error status

pivot scale in unit of 1/Mpc

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◆ comoving_radial_distance()

double comoving_radial_distance	(	struct Cosmology *	Cx,
		double	z
	)

Compute the comoving radial distance

Parameters

Cx	Input: pointer to Cosmology structure
z	Input: redshift to compute the spectrum

Returns: the double value D_c

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◆ concentration_cdm()

double concentration_cdm	(	double	M,
		double	z
	)

Compute the cold dark matter concentration-mass relation.

Parameters

M	Input: halo mass in unit of solar mass
z	Input: redshift of interest

Returns: the cdm concentration

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◆ Cosmology_free()

int Cosmology_free ( struct Cosmology * Cx )

Free the memory allocated to cosmology structure.

Parameters

Cx	Input: pointer to Cosmology structure

Returns: the error status

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◆ Cosmology_init()

int Cosmology_init	(	struct Cosmology *	Cx,
		double	pk_kmax,
		double	pk_zmax,
		int	nlines,
		int *	line_type,
		size_t	npoints_interp,
		double	M_min,
		long	mode_mf
	)

Allocate memory and initialize the cosmology structure, which includes the CLASS cosmology structure and line strucrure.

Parameters

Cx	Input: pointer to Cosmology structure
pk_kmax	Input: kmax for computation of matter power spectrum by CLASS
pk_zmax	Input: zmax for computation of matter power spectrum by CLASS
nlines	Input: number of lines whose properties we want to compute
line_type	Inpute: name of the line to compute. It can be set to CII, CO10, CO21, CO32, CO43, CO54, CO65
npoints_interp	Input: number of points in redshift for interpolation of line properties
M_min	Input: minimum halo mass for mass integrals
mode_mf	Inpute: theoretical model of halo mass function to use. It can be set to sheth-Tormen (ST), Tinker (TR) or Press-Schecter (PSC)

Returns: an integer if succeeded

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◆ der_lnsig_sq()

double der_lnsig_sq	(	struct Cosmology *	Cx,
		double	z,
		double	R
	)

Compute the logarithmic derivative of the variance of smoothed matter density fluctuations w.r.t.

smoothing scale

Parameters

Cx	Input: pointer to Cosmology structure
z	Input: redshift to compute the spectrum
R	Input: smoothing scale in unit of Mpc

Returns: the log-derivative of variance

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◆ derR_logwindow_g()

double derR_logwindow_g	(	double	k,
		double	R
	)

Derivative w.r.t smoothing scale of Gaussian window.

Parameters

k	Input: wavenumber in unit of 1/Mpc
R	Input: smoothing scale in unit of Mpc

Returns: the derivative of the window function

◆ derR_window_rth()

double derR_window_rth	(	double	k,
		double	R
	)

Derivative w.r.t.

smoothing scale of the Fourier transform of top-hat window in real space

Parameters

k	Input: wavenumber in unit of 1/Mpc
R	Input: smoothing scale in unit of Mpc

Returns: the derivative of the window function

◆ growth_D()

double growth_D	(	struct Cosmology *	Cx,
		double	k,
		double	z
	)

Compute the growth factor D(k,z) for a general case where it can be scale-dependant The scale-dep growth is calculated by taking the ratio of the transfer function at redshift z and zero.

cdm, baryon and total matter.

Parameters

Cx	Input: pointer to Cosmology structure
k	Input: wavenumbber in unit of 1/Mpc
z	Input: redshift to compute the spectrum

Returns: the growth factor, can be k-dep (ex. with nonzero neutrino mass)

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◆ growth_f()

double growth_f	(	struct Cosmology *	Cx,
		double	k,
		double	z
	)

Compute the growth factor D(k,z) by taking the ratio of the transfer function at redshift z and zero.

For a general case growth rate can be scale-dependant

Parameters

Cx	Input: pointer to Cosmology structure
k	Input: wavenumbber in unit of 1/Mpc
z	Input: redshift to compute the spectrum

Returns: the growth factor

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◆ Hubble()

double Hubble	(	struct Cosmology *	Cx,
		double	z
	)

Compute the the hubble rate (exactly the quantity defined by CLASS as index_bg_H in the background module).

Parameters

Cx	Input: pointer to Cosmology structure
z	Input: redshift to compute the spectrum

Returns: the hubble parameter

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◆ nfw_profile()

double nfw_profile	(	struct Cosmology *	Cx,
		double	k,
		double	M,
		double	z
	)

Compute the NFW halo profile in Fourier space, given by Eq.

3.7 of 2004.09515 The profile is normalized to unity at k->0, (see fig 3 of 1003.4740)

Parameters

Cx	Input: pointer to Cosmology structure
k	Input: wavenumber in unit of 1/Mpc
M	Input: halo mass in unit of solar mass
z	Input: redshift of interest

Returns: the nfw profile

rho_s is computed by enforcing int dr r^2 u(r) = 1

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◆ Pk_dlnPk_HV()

double Pk_dlnPk_HV	(	struct Cosmology *	Cx,
		double	k,
		double	z,
		int	mode
	)

Read in the linear power spectrum, used to set the initial conditions of Hidden-Valley sims.

Input k is in unit of 1/Mpc. First convert it to h/Mpc, and also convert the final matter power spectrum in unit of (Mpc/h)^3

Parameters

Cx	Input: pointer to Cosmology structure
k	Input: wavenumbber in unit of 1/Mpc
z	Input: redshift to compute the spectrum
mode	Input: switch to decide whether to evaluate the interpolator of the power spectrum or free the interpolator

Returns: the HV linear matter power spectrum

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◆ PS()

double PS	(	struct Cosmology *	Cx,
		double	k,
		double	z
	)

Evaluate the extrapolation for matter power spectrum beyond what is calculated by CLASS, same expansion as that used in CORE cosmology librrary (see arXiv:1812.05995) If requested k-value was beyond what is calculated by CLASS, this function extrapolates.

Parameters

Cx	Input: pointer to Cosmology structure
k	Input: wavenumbber in unit of 1/Mpc
z	Input: redshift to compute the spectrum

Returns: the double value of matter power spectrum

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◆ PS_class()

double PS_class	(	struct Cosmology *	Cx,
		double	k,
		double	z,
		long	mode
	)

Call CLASS-V3.1 functions to compute the cdm+b pk (in Mpc**3) for a given k (in 1/Mpc) and z In LIM_FISHER code, we always include massive neutrinos.

In this case, to compute the galaxy power spectrum, we should use cdm+b pk. Therefore hete when calling PS_class, we always get cdm+b pk, i.e. set &Cx -> ccs.fo.index_pk_cb. If you wanted to set neutrinos to be massless, you should replace this index by &Cx -> ccs.fo.index_pk_m The older routine of CLASS-v2.7, spectra_pk_at_k_and_z(), is replaced by fourier_pk_at_k_and_z(),

Input k is in unit of 1/Mpc. First convert it to h/Mpc, and also convert the final matter power spectrum in unit of (Mpc/h)^3

Parameters

Cx	Input: pointer to Cosmology structure
k	Input: wavenumbber in unit of 1/Mpc
z	Input: redshift to compute the spectrum
mode	Input: switch to decide whether to compute linear (LPOWER) or nonlinear (NLPOWER) spectrum

Returns: the double value of matter power spectrum

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◆ PS_xtrapol_free()

int PS_xtrapol_free ( struct PS_xtr * PS_xtrapol )

frees the interpolation elements for P_m spline

Parameters

PS_xtrapol Input: pointer to the structure containing the interpolation pointers

Returns: an integer indicating sucess

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◆ PS_xtrapol_init()

struct PS_xtr * PS_xtrapol_init ( struct Cosmology * Cx )

Call CLASS and build a 2d interpolator for Plin(k,z), which will be used when building an extrapolator for P(k,z) beyond a given kmax computed by CLASS.

Parameters

Cx	Input: pointer to Cosmology structure

Returns: a structure containing the interpolation pointers

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◆ R_scale()

double R_scale	(	struct Cosmology *	Cx,
		double	h_mass
	)

Compute the Lagrangian radius of halos in unit of Mpc , fixing z=0.

Parameters

Cx	Input: pointer to Cosmology structure
h_mass	Input: halo mass in unit of solar mass

Returns: R_s

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◆ R_scale_wrong()

double R_scale_wrong	(	struct Cosmology *	Cx,
		double	z,
		double	h_mass
	)

Compute the Lagrangian radius of halos in unit of Mpc at z.

Parameters

Cx	Input: pointer to Cosmology structure
z	Input: redshift
h_mass	Input: halo mass in unit of solar mass

Returns: R_s

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◆ R_vir()

double R_vir	(	struct Cosmology *	Cx,
		double	M
	)

Compute the comoving virial radius of halos in unit of Mpc, which is defined as the radius at which the average density within this radius is Delta X rho_c.

Parameters

Cx	Input: pointer to Cosmology structure
M	Input: halo mass in unit of solar mass

Returns: R_vir

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◆ rhoc()

double rhoc	(	struct Cosmology *	Cx,
		double	z
	)

Compute the critical density in unit of M_sun/Mpc^3.

Parameters

Cx	Input: pointer to Cosmology structure
z	Input: redshift to compute the spectrum

Returns: the double value of rho_c

E (a) = H(a)^2/H0^2

G is in unit of m^3 kg^-1 s^-2, conversion factor from m to Mpc

To convert to solar mass

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◆ scale_indep_growth_D()

double scale_indep_growth_D	(	struct Cosmology *	Cx,
		double	z
	)

Compute the growth factor D(k,z) which is scale-indep valid when neutrinos are massless The scale-dep growth is calculated by taking the ratio of the transfer function at redshift z and zero.

The scale-indep growth is computed by CLASS directly

Parameters

Cx	Input: pointer to Cosmology structure
z	Input: redshift to compute the spectrum

Returns: the growth factor, can be k-dep (ex. with nonzero neutrino mass)

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◆ scale_indep_growth_f()

double scale_indep_growth_f	(	struct Cosmology *	Cx,
		double	z
	)

Compute the scale-independent growth rate f(z) which is scale-indep valid when neutrinos are massless.

Parameters

Cx	Input: pointer to Cosmology structure
z	Input: redshift to compute the spectrum

Returns: the growth factor

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◆ sig_sq()

double sig_sq	(	struct Cosmology *	Cx,
		double	z,
		double	R
	)

Compute variance of smoothed matter density fluctuations.

The function sigma0_integrand() defines the integrand and sigma0_sq() computes the k-integral

Parameters

Cx	Input: pointer to Cosmology structure
z	Input: redshift to compute the spectrum
R	Input: smoothing scale

Returns: the unsmoothed variance

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◆ sig_sq_integrand()

double sig_sq_integrand	(	double	x,
		void *	par
	)

The integrand function passed to qags integrator to compute the variance of the smoothed matter density.

Parameters

x	Input: integration variable
par	Input: integration parmaeters

Returns: value of the integrand

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◆ sigma0_sq()

double sigma0_sq	(	struct Cosmology *	Cx,
		double	z,
		double	kmax
	)

Compute variance of unsmoothed matter density fluctuations.

The function sigma0_integrand() defines the integrand and sigma0_sq() computes the k-integral

Parameters

Cx	Input: pointer to Cosmology structure
kmax	Input: maximum wavenumber in unit of 1/Mpc
z	Input: redshift to compute the spectrum

Returns: the unsmoothed variance

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◆ sigma0_sq_integrand()

double sigma0_sq_integrand	(	double	x,
		void *	par
	)

The integrand function passed to qags integrator to compute the variance of the unsmoothed matter density.

Parameters

x	Input: integration variable
par	Input: integration parmaeters

Returns: value of the integrand

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◆ transfer()

double transfer	(	struct Cosmology *	Cx,
		double	k,
		double	z,
		int	mode
	)

call CLASS-V3.1 to compute transfer function for different species depending on the switch "mode" mode can be set to cdm, baryons or total matter transfer function.

The older routine of CLASS-v2.7, spectra_tk_at_k_and_z(), is replaced by perturbations_sources_at_k_and_z(), which evaluates the matter transfer functions at a given value of k and z

Parameters

Cx	Input: pointer to Cosmology structure
k	Input: wavenumbber in unit of 1/Mpc
z	Input: redshift to compute the spectrum
mode	Input: switch to decide which species to consider, can be set to cdm, baryons or total matter transfer function.

Returns: the transfer function of a given species

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◆ window_g()

double window_g	(	double	k,
		double	R
	)

Gaussian window.

Parameters

k	Input: wavenumber in unit of 1/Mpc
R	Input: smoothing scale in unit of Mpc

Returns: the window function

◆ window_kth()

double window_kth	(	double	k,
		double	R
	)

Top-hat window in Fourier space.

Parameters

k	Input: wavenumber in unit of 1/Mpc
R	Input: smoothing scale in unit of Mpc

Returns: the window function

◆ window_rth()

double window_rth	(	double	k,
		double	R
	)

Fourier transform of top-hat window in real space.

Parameters

k	Input: wavenumber in unit of 1/Mpc
R	Input: smoothing scale in unit of Mpc

Returns: the window function

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Functions

Detailed Description

Function Documentation

◆ angular_distance()

◆ CL_Cosmology_free()

◆ CL_Cosmology_initilize()

◆ comoving_radial_distance()

◆ concentration_cdm()

◆ Cosmology_free()

◆ Cosmology_init()

◆ der_lnsig_sq()

◆ derR_logwindow_g()

◆ derR_window_rth()

◆ growth_D()

◆ growth_f()

◆ Hubble()

◆ nfw_profile()

◆ Pk_dlnPk_HV()

◆ PS()

◆ PS_class()

◆ PS_xtrapol_free()

◆ PS_xtrapol_init()

◆ R_scale()

◆ R_scale_wrong()

◆ R_vir()

◆ rhoc()

◆ scale_indep_growth_D()

◆ scale_indep_growth_f()

◆ sig_sq()

◆ sig_sq_integrand()

◆ sigma0_sq()

◆ sigma0_sq_integrand()

◆ transfer()

◆ window_g()

◆ window_kth()

◆ window_rth()