zeus21.cosmology

Cosmology functions and helper tools related with cosmology.

Authors: zeus21 v2 collaboration - June 2026: Emily Bregou ; Hector Afonso G. Cruz ; Sarah Libanore ; Julian B. Muñoz ; Yonny Sklansky ; Emilie Thélie ; Alessandra Venditti

arXiv:2302.08506, arXiv:2306.09403, arXiv:2407.18294, Sklansky et al. (in prep)

Classes

HMF_interpolator

Class that builds an interpolator of the HMF as function of the halo mass and redshift.

Functions

`time_at_redshift`(ClassyCosmo, z)	Returns the age of the Universe (in Gyrs) corresponding to a given redshift.
`redshift_at_time`(ClassyCosmo, t)	Returns the redshift corresponding to a given age of the Universe (in Gyrs).
`Hub`(CosmoParams, z)	Hubble parameter H(z).
`HubinvMpc`(CosmoParams, z)	Converts Hubble parameter H(z) in inverse length units (1/Mpc).
`Hubinvyr`(CosmoParams, z)	Converts Hubble parameter H(z) in inverse time units (1/yr).
`rho_baryon`(CosmoParams, z)	Baryon density rho_baryon(z).
`n_H`(CosmoParams, z)	Number density of hydrogen nuclei (including both neutral or ionized).
`Tcmb`(ClassCosmo, z)	CMB temperature T(z).
`Tadiabatic`(CosmoParams, z)	Returns T_adiabatic as a function of z from thermodynamics in CLASS.
`xefid`(CosmoParams, z)	Electron fraction x_e(z) without any sources.
`adiabatic_index`(z)	Returns adiabatic index (delta_Tad/delta) as a function of z. Fit from 1506.04152. to ~3% on z = 6 − 50).
`MhofRad`(CosmoParams, R)	Convert input comoving Radius to virial Mass.
`RadofMh`(CosmoParams, M)	Convert input virial Mass to comoving Radius.
`ST_HMF`(CosmoParams, Mass, sigmaM, dsigmadM)	Sheth-Tormen Halo Mass Function.
`Tink_HMF`(CosmoParams, Mass, sigmaM, dsigmadM, z)	Tinker 2008 Halo Mass Function.
`f_GUREFT_physical`(sigmaM, z)	Fit in eq A2 in Yung+23 (2309.14408) to z < 20.
`PS_HMF_unnorm`(CosmoParams, Mass, nu, dlogSdM)	Unnormalized Press-Schechter HMF.
`growth`(CosmoParams, z)	Interpolator to find the scale-independent growth factor.
`dgrowth_dz`(CosmoParams, z)	Derivative of growth factor w.r.t. z.
`redshift_of_chi`(CosmoParams, chi)	Redshift associated with the given comoving distance in the input cosmology.
`chi_of_redshift`(CosmoParams, z)	Comoving distance associated with given redshift in the input cosmology.
`T021`(CosmoParams, z)	Prefactor in mK to T21 that only depends on cosmological parameters and z. See Eq.(21) in 2110.13919
`bias_ST`(CosmoParams, sigmaM)	Bias of halos in the Sheth-Tormen model.
`bias_Tinker`(CosmoParams, sigmaM)	Bias of halos in the Tinker model. See https://arxiv.org/pdf/1001.3162.pdf for Delta = 200

Module Contents

zeus21.cosmology.time_at_redshift(ClassyCosmo, z)[source]

Returns the age of the Universe (in Gyrs) corresponding to a given redshift.

Parameters:

ClassyCosmo (zeus21.runclass class) – Sets up Class cosmology.
z (float) – Redshift.

Returns:

Age of the Universe in Gyrs.

Return type:

float

zeus21.cosmology.redshift_at_time(ClassyCosmo, t)[source]

Returns the redshift corresponding to a given age of the Universe (in Gyrs).

Parameters:

ClassyCosmo (zeus21.runclass class) – Sets up Class cosmology.
t (float) – Age in Gyrs.

Returns:

Redshift corresponding to the given age of the Universe.

Return type:

float

zeus21.cosmology.Hub(CosmoParams, z)[source]

Hubble parameter H(z).

Parameters:

CosmoParams (CosmoParams) – Cosmological parameters.
z (float) – Redshift.

Returns:

Hubble parameter H(z) in km/s/Mpc.

Return type:

float

zeus21.cosmology.HubinvMpc(CosmoParams, z)[source]

Converts Hubble parameter H(z) in inverse length units (1/Mpc).

Parameters:

CosmoParams (CosmoParams) – Cosmological parameters.
z (float) – Redshift.

Returns:

Hubble parameter H(z) in 1/Mpc.

Return type:

float

zeus21.cosmology.Hubinvyr(CosmoParams, z)[source]

Converts Hubble parameter H(z) in inverse time units (1/yr).

Parameters:

CosmoParams (CosmoParams) – Cosmological parameters.
z (float) – Redshift.

Returns:

Hubble parameter H(z) in 1/yr.

Return type:

float

zeus21.cosmology.rho_baryon(CosmoParams, z)[source]

Baryon density rho_baryon(z).

Parameters:

CosmoParams (CosmoParams) – Cosmological parameters.
z (float) – Redshift.

Returns:

Baryon density rho_baryon(z) in Msun/Mpc^3.

Return type:

float

zeus21.cosmology.n_H(CosmoParams, z)[source]

Number density of hydrogen nuclei (including both neutral or ionized).

Parameters:

CosmoParams (CosmoParams) – Cosmological parameters.
z (float) – Redshift.

Returns:

Number density of hydrogen nuclei in 1/cm^3.

Return type:

float

zeus21.cosmology.Tcmb(ClassCosmo, z)[source]

CMB temperature T(z).

Parameters:

ClassCosmo (ClassCosmo) – CLASS cosmology object.
z (float) – Redshift.

Returns:

CMB temperature T(z) in K.

Return type:

float

zeus21.cosmology.Tadiabatic(CosmoParams, z)[source]

Returns T_adiabatic as a function of z from thermodynamics in CLASS.

Parameters:

CosmoParams (CosmoParams) – Cosmological parameters.
z (float) – Redshift.

Returns:

Adiabatic temperature T_adiabatic(z).

Return type:

float

zeus21.cosmology.xefid(CosmoParams, z)[source]

Electron fraction x_e(z) without any sources. Uses thermodynamics in CLASS for z>15, and fixed below to avoid the tanh approximation.

Parameters:

CosmoParams (CosmoParams) – Cosmological parameters.
z (float) – Redshift.

Returns:

Fiducial x_e(z).

Return type:

float

zeus21.cosmology.adiabatic_index(z)[source]

Returns adiabatic index (delta_Tad/delta) as a function of z. Fit from 1506.04152. to ~3% on z = 6 − 50).

Parameters:: z (float) – Redshift.
Returns:: Adiabatic index (delta_Tad/delta).
Return type:: float

zeus21.cosmology.MhofRad(CosmoParams, R)[source]

Convert input comoving Radius to virial Mass.

Parameters:

CosmoParams (CosmoParams) – Cosmological parameters.
R (float) – Comoving radius in cMpc.

Returns:

Mass in Msun.

Return type:

float

zeus21.cosmology.RadofMh(CosmoParams, M)[source]

Convert input virial Mass to comoving Radius.

Parameters:

CosmoParams (CosmoParams) – Cosmological parameters.
M (float) – Virial mass in Msun.

Returns:

Comoving radius in cMpc.

Return type:

float

zeus21.cosmology.ST_HMF(CosmoParams, Mass, sigmaM, dsigmadM)[source]

Sheth-Tormen Halo Mass Function.

Parameters:

CosmoParams (CosmoParams) – Cosmological parameters.
Mass (float) – Halo mass in Msun.
sigmaM (float) – Variance of the density field on the scale of the halo mass.
dsigmadM (float) – Derivative of sigmaM with respect to Mass.

Returns:

HMF value in 1/Mpc^3/Msun.

Return type:

float

zeus21.cosmology.Tink_HMF(CosmoParams, Mass, sigmaM, dsigmadM, z)[source]

Tinker 2008 Halo Mass Function. All in physical (no h) units. Form from App.A of Yung+23 (2309.14408).

Parameters:

CosmoParams (CosmoParams) – Cosmological parameters.
Mass (float) – Halo mass in Msun.
sigmaM (float) – Variance of the density field on the scale of the halo mass at redshift z.
dsigmadM (float) – Derivative of sigmaM with respect to Mass at redshift z.
z (float) – Redshift.

Returns:

HMF value in 1/Mpc^3/Msun.

Return type:

float

zeus21.cosmology.f_GUREFT_physical(sigmaM, z)[source]

Fit in eq A2 in Yung+23 (2309.14408) to z < 20. Required by the Tinker 2008 HMF; all in physical units (no h). Implementation thanks to Aaron Yung.

Parameters:

sigmaM (float) – Variance of the density field on the scale of the halo mass at redshift z.
z (float) – Redshift.

Returns:

HMF value in 1/Mpc^3/Msun.

Return type:

float

zeus21.cosmology.PS_HMF_unnorm(CosmoParams, Mass, nu, dlogSdM)[source]

Unnormalized Press-Schechter HMF. Used to emulate 21cmFAST.

Parameters:

CosmoParams (CosmoParams) – Cosmological parameters.
Mass (float) – Halo mass in Msun.
nu (float) – Peak height, defined as nu = delta_tilde/S_tilde, with delta_tilde = delta_crit - delta_R, and variance S = sigma(M)^2 - sigma(R)^2.
dlogSdM (float) – Derivative of log(S) with respect to Mass, where S = sigma(M)^2 - sigma(R)^2.

Returns:

HMF value in 1/Mpc^3/Msun.

Return type:

float

class zeus21.cosmology.HMF_interpolator(UserParams, CosmoParams)[source]

Class that builds an interpolator of the HMF as function of the halo mass and redshift.

Parameters:

UserParams (UserParams) – User parameters, used to set the resolution of the HMF table.
CosmoParams (CosmoParams) – Cosmological parameters, used to compute the HMF table with CLASS.

HMF_int[source]

Interpolator for HMF value, takes (Mass, z) as arguments

Type:: RegularGridInterpolator

sigma_int[source]

Interpolator for sigma value, takes (Mass, z) as arguments

Type:: RegularGridInterpolator

sigmaR_int[source]

Interpolator for sigma(R) value, takes (R, z) as arguments

Type:: RegularGridInterpolator

dsigmadM_int[source]

Interpolator for dsigma/dM value, takes (Mass, z) as arguments

Type:: RegularGridInterpolator

Mhtab[source]

logtabMh[source]

RMhtab[source]

zHMFtab[source]

sigmaMhtab[source]

dsigmadMMhtab[source]

HMFtab[source]

fitMztab[source]

logHMFint[source]

sigmaintlog[source]

dsigmadMintlog[source]

sigmaofRtab[source]

fitRztab[source]

sigmaRintlog[source]

HMF_int(Mh, z)[source]

Interpolator to find HMF(M,z).

Parameters:

Mh (float or array) – Halo mass in Msun. Can be a single value or an array of values.
z (float)

Returns:

Interpolator for HMF value, takes (Mass, z) as arguments.

Return type:

float

sigma_int(Mh, z)[source]

Interpolator to find sigma(M,z).

Parameters:

Mh (float or array) – Halo mass in Msun. Can be a single value or an array of values.
z (float)

Returns:

Interpolator for sigma value, takes (Mass, z) as arguments.

Return type:

float

sigmaR_int(RR, z)[source]

Interpolator to find sigma(R,z).

Parameters:

RR (float or array) – Comoving distance in Mpc. Can be a single value or an array of values.
z (float)

Returns:

Interpolator for sigma value, takes (R, z) as arguments.

Return type:

float

dsigmadM_int(Mh, z)[source]

Interpolator to find dsigma/dM.

Parameters:

Mh (float or array) – Halo mass in Msun. Can be a single value or an array of values.
z (float)

Returns:

Interpolator for dsigma/dM value, takes (Mass, z) as arguments.

Return type:

float

zeus21.cosmology.growth(CosmoParams, z)[source]

Interpolator to find the scale-independent growth factor.

Parameters:

CosmoParams (CosmoParams) – Cosmological parameters, used to compute the growth factor with CLASS.
z (float) – Redshift.

Returns:

Interpolator for the scale-independent growth factor, takes z as argument.

Return type:

float

zeus21.cosmology.dgrowth_dz(CosmoParams, z)[source]

Derivative of growth factor w.r.t. z.

Parameters:

CosmoParams (CosmoParams) – Cosmological parameters, used to compute the growth factor with CLASS.
z (float) – Redshift.

Returns:

dgrowth/dz

Return type:

float

zeus21.cosmology.redshift_of_chi(CosmoParams, chi)[source]

Redshift associated with the given comoving distance in the input cosmology.: This function is not used inside the code but is provided for users

Parameters:

CosmoParams (CosmoParams) – Cosmological parameters, used to compute the growth factor with CLASS.
chi (float) – Comoving distance from today in Mpc

Returns:

z – Redshift

Return type:

float

zeus21.cosmology.chi_of_redshift(CosmoParams, z)[source]

Comoving distance associated with given redshift in the input cosmology. This function is not used inside the code but is provided for users

Parameters:

CosmoParams (CosmoParams) – Cosmological parameters, used to compute the growth factor with CLASS.
z (float) – Redshift

Returns:

chi – Comoving distance from today in Mpc

Return type:

float

zeus21.cosmology.T021(CosmoParams, z)[source]

Prefactor in mK to T21 that only depends on cosmological parameters and z. See Eq.(21) in 2110.13919

Parameters:

CosmoParams (CosmoParams) – Cosmological parameters, used to compute the growth factor with CLASS.
z (float) – Redshift.

Returns:

Prefactor in mK to T21

Return type:

float

zeus21.cosmology.bias_ST(CosmoParams, sigmaM)[source]

Bias of halos in the Sheth-Tormen model. See https://arxiv.org/pdf/1007.4201.pdf Table 1

Parameters:

CosmoParams (CosmoParams) – Cosmological parameters, used to compute the growth factor with CLASS.
sigmaM (float) – Variance of the matter density field smoothed on a scale corresponding to the halo mass.

Returns:

Halo bias

Return type:

float

zeus21.cosmology.bias_Tinker(CosmoParams, sigmaM)[source]

Bias of halos in the Tinker model. See https://arxiv.org/pdf/1001.3162.pdf for Delta = 200

Parameters:

CosmoParams (CosmoParams) – Cosmological parameters, used to compute the growth factor with CLASS.
sigmaM (float) – Variance of the matter density field smoothed on a scale corresponding to the halo mass.

Returns:

Halo bias

Return type:

float