hmfast.cosmology.Cosmology

class hmfast.cosmology.Cosmology(emulator_set='lcdm:v1', H0=68.0, omega_cdm=0.12, omega_b=0.02246576, A_s=2.1053e-09, n_s=0.965, tau=0.0544, m_ncdm=0.06, N_ur=3.046, w0=-0.95, f_ede=0.1, z_c=3162.278, theta_i=1.57, r=0.01, T_cmb=2.7255, deg_ncdm=1.0)[source]

Bases: object

Cosmology model and emulator interface.

Provides access to cosmological parameters and emulator-based predictions for distances, Hubble parameter, power spectra, CMB spectra, and derived parameters. Note that using parameters outside the emulator training bounds will result in NaN outputs.

Attributes:

emulator_setstr: Emulator-set identifier selecting the corresponding emulator set. Allowed values are "lcdm:v1", "mnu:v1", "neff:v1", "wcdm:v1", "ede:v1", "mnu-3states:v1", and "ede:v2".
H0float: Hubble constant at \(z = 0\) in units of \(\mathrm{km} \, \mathrm{s}^{-1} \, \mathrm{Mpc}^{-1}\).
omega_cdmfloat: Physical cold dark matter density, \(\omega_{\mathrm{cdm}} = \Omega_{\mathrm{cdm}} h^2\).
omega_bfloat: Physical baryon density, \(\omega_b = \Omega_b h^2\).
A_sfloat: Amplitude of the primordial scalar power spectrum, \(A_s\).
n_sfloat: Scalar spectral index of primordial perturbations, \(n_s\).
taufloat: Optical depth to reionization, \(\tau\).
m_ncdmfloat: Total non-cold dark matter mass, used if a massive-neutrino cosmological model is selected.
N_urfloat: Effective number of ultra-relativistic species, \(N_{\mathrm{ur}}\), used if a model with additional radiation degrees of freedom is selected.
w0float: Present-day dark energy equation-of-state parameter \(w_0\), used if a cosmological model with dark energy equation-of-state parameter \(w_0\) is selected.
f_edefloat: Maximum fractional contribution of early dark energy, \(f_{\mathrm{ede}}\), used if an early dark energy cosmological model is selected.
z_cfloat: Critical redshift for the early dark energy transition, \(z_c\), used if an early dark energy cosmological model is selected.
theta_ifloat: Initial scalar field displacement for the early dark energy model, \(\theta_i\), in radians, used if an early dark energy cosmological model is selected.
rfloat: Tensor-to-scalar ratio, used if a cosmological model including primordial tensors is selected.
T_cmbfloat: CMB temperature today in Kelvin, used when non-emulator background quantities require it.
deg_ncdmfloat: Degeneracy factor for the non-cold dark matter species, used if a massive-neutrino cosmological model is selected.

Methods

`angular_diameter_distance`(z)	Get angular diameter distance \(D_A(z)\) at redshift \(z\) from the emulator.
`cl`(type, l)	Evaluate the CMB power spectrum of the specified type at requested multipoles l using the emulator.
`comoving_volume_element`(z)	Comoving volume element per unit redshift and solid angle.
`critical_density`(z)	Get critical density \(\rho_{\mathrm{crit}}(z)\) at redshift \(z\).
`delta_c`(z[, prescription])	Spherical-collapse threshold \(\delta_c(z)\).
`derived_parameters`()	Get derived cosmological parameters from the emulator.
`growth_factor`(z)	Linear growth factor \(D(z)\), normalized to \(D(0)=1\).
`growth_rate`(z)	Linear growth rate
`hubble_parameter`(z)	Get Hubble parameter \(H(z)\) at redshift \(z\) from the emulator.
`omega_m`(z)	Matter density parameter excluding neutrinos.
`pk`(k, z[, linear])	Get the matter power spectrum \(P(k, z)\) interpolated at requested wavenumbers k and redshifts z.
`sigma8`(z)	Get \(\sigma_8(z)\) at redshift \(z\) from the emulator.
`sigma_m`(m, z)	Evaluate \(\sigma(M, z)\) on a physical mass-redshift grid.
`sigma_r`(r, z)	Evaluate \(\sigma(R, z)\) on a physical radius-redshift grid.
`update`([H0, omega_cdm, omega_b, A_s, n_s, ...])	Return a new Cosmology instance with updated parameters.
`velocity_dispersion`(z)	Compute the dimensionless velocity dispersion

update(H0=None, omega_cdm=None, omega_b=None, A_s=None, n_s=None, tau=None, m_ncdm=None, N_ur=None, w0=None, f_ede=None, z_c=None, theta_i=None, r=None, T_cmb=None, deg_ncdm=None)[source]

Return a new Cosmology instance with updated parameters.

Each parameter defaults to None. Only those not None are updated.

Parameters:

H0, omega_cdm, omega_b, A_s, n_s, tau, m_ncdm, N_ur, w0, f_ede, z_c, theta_i, r, T_cmb, deg_ncdmfloat or None: Cosmological parameters to update. In particular, \(\tau\) is the optical depth to reionization and \(\theta_i\) is the initial early-dark-energy scalar field displacement.

Returns:

Cosmology: New instance with updated parameters.

sigma_m(m, z)[source]

Evaluate \(\sigma(M, z)\) on a physical mass-redshift grid.

The variance is defined by

\[\sigma^2(M, z) = \frac{1}{2\pi^2} \int_0^\infty dk\, k^2\, P_{\mathrm{L}}(k, z)\, \hat{W}^2(kR),\]

with Fourier-space top-hat window

\[\hat{W}(x) = \frac{3}{x^3}\left[\sin x - x \cos x\right].\]

Parameters:

mfloat or jnp.ndarray: Halo mass or mass grid in physical \(M_\odot\).
zfloat or jnp.ndarray: Redshift or redshift grid.

Returns:

float or jnp.ndarray: Values of \(\sigma(M, z)\) with shape \((N_m, N_z)\), where singleton dimensions get squeezed before return.

sigma_r(r, z)[source]

Evaluate \(\sigma(R, z)\) on a physical radius-redshift grid.

The variance is defined by

\[\sigma^2(R, z) = \frac{1}{2\pi^2} \int_0^\infty dk\, k^2\, P_{\mathrm{L}}(k, z)\, \hat{W}^2(kR),\]

with Fourier-space top-hat window

\[\hat{W}(x) = \frac{3}{x^3}\left[\sin x - x \cos x\right].\]

Parameters:

rfloat or jnp.ndarray: Comoving top-hat radius or radius grid in physical \(\mathrm{Mpc}\).
zfloat or jnp.ndarray: Redshift or redshift grid.

Returns:

float or jnp.ndarray: Values of \(\sigma(R, z)\) with shape \((N_r, N_z)\), where singleton dimensions get squeezed before return.

hubble_parameter(z)[source]

Get Hubble parameter \(H(z)\) at redshift \(z\) from the emulator.

Parameters:

zfloat or jnp.ndarray: Redshift(s)

Returns:

jnp.ndarray: Hubble parameter(s) in \(\mathrm{km} \, \mathrm{s}^{-1} \, \mathrm{Mpc}^{-1}\)

angular_diameter_distance(z)[source]

Get angular diameter distance \(D_A(z)\) at redshift \(z\) from the emulator.

Parameters:

zfloat or jnp.ndarray: Redshift(s)

Returns:

jnp.ndarray: Angular diameter distance(s) in \(\mathrm{Mpc}\).

sigma8(z)[source]

Get \(\sigma_8(z)\) at redshift \(z\) from the emulator.

\(\sigma_8(z)\) is the dimensionless root-mean-square linear matter fluctuation amplitude in spheres of radius \(8 \, \mathrm{Mpc}/h\).

Parameters:

zfloat or jnp.ndarray: Redshift(s)

Returns:

jnp.ndarray: Dimensionless \(\sigma_8\) value(s)

critical_density(z)[source]

Get critical density \(\rho_{\mathrm{crit}}(z)\) at redshift \(z\).

\[\rho_{\mathrm{crit}}(z) = \frac{3 H(z)^2}{8 \pi G}\]

Parameters:

zfloat or jnp.ndarray: Redshift(s)

Returns:

jnp.ndarray: Critical density in \(M_\odot \, \mathrm{Mpc}^{-3}\)

omega_m(z)[source]

Matter density parameter excluding neutrinos.

\[\Omega_m(z) = \frac{\Omega_{m,\mathrm{no\nu},0}(1+z)^3}{\Omega_{m,0}(1+z)^3 + \Omega_{\Lambda,0} + \Omega_{r,0}(1+z)^4}\]

Parameters:

zfloat or jnp.ndarray: Redshift(s)

Returns:

float or jnp.ndarray: Dimensionless matter density at redshift \(z\)

delta_c(z, prescription='EdS')[source]

Spherical-collapse threshold \(\delta_c(z)\).

Supported prescriptions are:

"EdS" for the Einstein-de Sitter exact value, \(\delta_c = \frac{3}{20}(12\pi)^{2/3}\).
"EdS_approx" for the standard Einstein-de Sitter approximation, \(\delta_c = 1.686\).
"NS97" for the Nakamura and Suto (1997) fit,

\[\delta_c(z) = \frac{3}{20}(12\pi)^{2/3} \left[1 + 0.012299 \, \log_{10}(\Omega_m(z))\right].\]

Parameters:

zfloat or jnp.ndarray: Redshift(s).
prescriptionstr, optional: Collapse-threshold prescription. Supported values are "EdS", "EdS_approx", and "NS97". Input is case-insensitive.

Returns:

float or jnp.ndarray: Collapse threshold evaluated at \(z\).

growth_factor(z)[source]

Linear growth factor \(D(z)\), normalized to \(D(0)=1\).

Parameters:

zfloat or jnp.ndarray: Redshift(s)

Returns:

jnp.ndarray: Dimensionless linear growth factor at \(z\), with shape \((N_z,)\), where singleton dimensions get squeezed before return.

growth_rate(z)[source]

Linear growth rate

\[f(z) = \frac{d \ln D}{d \ln a}\]

Parameters:

zfloat or jnp.ndarray: Redshift(s)

Returns:

jnp.ndarray: Dimensionless linear growth rate at \(z\), with shape \((N_z,)\), where singleton dimensions get squeezed before return.

velocity_dispersion(z)[source]

Compute the dimensionless velocity dispersion

\[\frac{1}{3} \frac{v_\mathrm{rms}^2}{c^2}\]

from the linear growth factor and matter power spectrum.

Parameters:

zfloat or jnp.ndarray: Redshift(s)

Returns:

jnp.ndarray: Dimensionless velocity dispersion at \(z\), equal to \(\frac{1}{3} \frac{v_\mathrm{rms}^2}{c^2}\), with shape \((N_z,)\), where singleton dimensions get squeezed before return.

comoving_volume_element(z)[source]

Comoving volume element per unit redshift and solid angle.

\[\frac{dV}{dz\,d\Omega} = \frac{(1+z)^2\, D_A(z)^2 \, c}{H(z)}\]

Parameters:

zfloat or jnp.ndarray: Redshift(s)

Returns:

float or jnp.ndarray: \(\frac{dV}{dz\,d\Omega}\) in \(\mathrm{Mpc}^3 \, \mathrm{sr}^{-1}\)

pk(k, z, linear=True)[source]

Get the matter power spectrum \(P(k, z)\) interpolated at requested wavenumbers k and redshifts z.

Parameters:

kfloat or jnp.ndarray: Wavenumber(s) in \(\mathrm{Mpc}^{-1}\) to evaluate the power spectrum at.
zfloat or jnp.ndarray: Redshift(s) at which to evaluate the power spectrum.
linearbool: True for linear \(P(k)\), False for nonlinear \(P(k)\).

Returns:

Pjnp.ndarray: Power spectrum values with shape \((N_k, N_z)\), where singleton dimensions get squeezed before return.

cl(type, l)[source]

Evaluate the CMB power spectrum of the specified type at requested multipoles l using the emulator. This method can be used to evaluate \(C_\ell^{TT}\), \(C_\ell^{EE}\), \(C_\ell^{TE}\), and \(C_\ell^{\phi\phi}\) by passing the appropriate type argument.

Parameters:

typestr: Power-spectrum specifier, e.g. ‘TT’, ‘EE’, ‘TE’, or ‘PP’. Case-insensitive.
lint or array-like: Multipole(s) at which to evaluate C_ell.

Returns:

jnp.ndarray: C_ell for the requested type evaluated at l. Out-of-range l return NaN.

derived_parameters()[source]

Get derived cosmological parameters from the emulator.

Returns:

dict

Dictionary of derived parameters with the following keys:

‘100*theta_s’ : Sound horizon angle (in units of 1/100 radians)
‘sigma8’ : Dimensionless RMS linear matter fluctuation in 8 Mpc/h spheres
‘YHe’ : Primordial helium fraction
‘z_reio’ : Redshift of reionization
‘Neff’ : Effective number of relativistic species
‘tau_rec’ : Conformal time at recombination (maximum visibility)
‘z_rec’ : Redshift at recombination (maximum visibility)
‘rs_rec’ : Comoving sound horizon at recombination [Mpc]
‘chi_rec’ : Comoving distance to recombination [Mpc]
‘tau_star’ : Conformal time at last scattering (optical depth = 1)
‘z_star’ : Redshift at last scattering (optical depth = 1)
‘rs_star’ : Comoving sound horizon at last scattering [Mpc]
‘chi_star’ : Comoving distance to last scattering [Mpc]
‘rs_drag’ : Comoving sound horizon at baryon drag [Mpc]