wcosmo.astropy.FlatwCDM

class wcosmo.astropy.FlatwCDM(H0, Om0, w0=-1, Tcmb0=None, Neff=None, m_nu=None, Ob0=None, *, zmin=0.0001, zmax=100, method='pade', name=None, meta=None)

Bases: WCosmoMixin

__init__(H0, Om0, w0=-1, Tcmb0=None, Neff=None, m_nu=None, Ob0=None, *, zmin=0.0001, zmax=100, method='pade', name=None, meta=None)

FLRW cosmology with a constant dark energy EoS and no spatial curvature.

This has one additional attribute beyond those of FLRW.

Docstring copied from astropy.cosmology.flrw.wcdm.FlatwCDM

Parameters:

H0float or scalar quantity-like [‘frequency’]

Hubble constant at z = 0. If a float, must be in [km/sec/Mpc].

Om0float

Omega matter: density of non-relativistic matter in units of the critical density at z=0.

w0float, optional

Dark energy equation of state at all redshifts. This is pressure/density for dark energy in units where c=1. A cosmological constant has w0=-1.0.

Tcmb0float or scalar quantity-like [‘temperature’], optional

Temperature of the CMB z=0. If a float, must be in [K]. Default: 0 [K]. Setting this to zero will turn off both photons and neutrinos (even massive ones).

Nefffloat, optional

Effective number of Neutrino species. Default 3.04.

m_nuquantity-like [‘energy’, ‘mass’] or array-like, optional

Mass of each neutrino species in [eV] (mass-energy equivalency enabled). If this is a scalar Quantity, then all neutrino species are assumed to have that mass. Otherwise, the mass of each species. The actual number of neutrino species (and hence the number of elements of m_nu if it is not scalar) must be the floor of Neff. Typically this means you should provide three neutrino masses unless you are considering something like a sterile neutrino.

Ob0float or None, optional

Omega baryons: density of baryonic matter in units of the critical density at z=0. If this is set to None (the default), any computation that requires its value will raise an exception.

method: str (optional, keyword-only)

The integration method, should be one of pade or analytic for the pade approximation or analytic hypergeometric methods respectively.

namestr or None (optional, keyword-only)

Name for this cosmological object.

metamapping or None (optional, keyword-only)

Metadata for the cosmology, e.g., a reference.

Examples

>>> from astropy.cosmology import FlatwCDM
>>> cosmo = FlatwCDM(H0=70, Om0=0.3, w0=-0.9)

The comoving distance in Mpc at redshift z:

>>> z = 0.5
>>> dc = cosmo.comoving_distance(z)

Methods

H(z)	Compute the Hubble parameter \(H(z)\) for a flat wCDM cosmology.
__init__(H0, Om0[, w0, Tcmb0, Neff, m_nu, ...])	FLRW cosmology with a constant dark energy EoS and no spatial curvature.
absorption_distance(z)	Compute the absorption distance using an analytic integral of the Pade approximation.
age(z[, zmax])	Compute the age of the universe at redshift z.
comoving_distance(z)	Compute the comoving distance using an analytic integral of the Pade approximation.
comoving_transverse_distance(z)	Compute the comoving distance using an analytic integral of the Pade approximation.
comoving_volume(z)	Compute the comoving volume out to redshift z.
dDLdz(z)	The Jacobian for the conversion of redshift to luminosity distance.
dLdH(z)	Derivative of the luminosity distance w.r.t.
de_density_scale(z)	Dark energy density at redshift z.
detector_to_source_frame(m1z, m2z, dL[, ...])	Convert masses and luminosity distance from the detector frame to source frame masses and redshift.
differential_comoving_volume(z)	Compute the differential comoving volume element.
distmod(z)	Compute the distance modulus at redshift z.
efunc(z)	Compute the \(E(z)\) function for a flat wCDM cosmology.
inv_efunc(z)	Compute the inverse of the E(z) function for a flat wCDM cosmology.
lookback_time(z)	Compute the lookback time using an analytic integral of the Pade approximation.
luminosity_distance(z)	Compute the luminosity distance using an analytic integral of the Pade approximation.
source_to_detector_frame(m1, m2, z)	Convert masses and redshift from the source frame to the detector frame.

Attributes

H0
hubble_distance	Compute the Hubble distance \(D_H = c H_0^{-1}\) in Mpc.
hubble_time	Compute the Hubble time \(t_H = H_0^{-1}\) in Gyr.

H(z)

Compute the Hubble parameter \(H(z)\) for a flat wCDM cosmology.

\[H(z; H_0, \Omega_{m,0}, w_0) = \frac{d_H(H_0)}{E(z; \Omega_{m,0}, w_0)}\]

Parameters:

z: array_like

Redshift

Returns:

H(z): array_like

The Hubble parameter

absorption_distance(z)

Compute the absorption distance using an analytic integral of the Pade approximation.

\[d_{A} = \int_{0}^{z} \frac{dz' (1 + z')^2}{E(z'; \Omega_{m,0}, w_0)}\]

Parameters:

z: array_like

Redshift

Returns:

absorption_distance: array_like

The absorption distance in Mpc

age(z, zmax=100000.0)

Compute the age of the universe at redshift z.

Parameters:

z: array_like

Redshift

zmax: float, optional

The maximum redshift to consider, default is 1e5

Returns:

age: array_like

The age of the universe in Gyr

comoving_distance(z)

Compute the comoving distance using an analytic integral of the Pade approximation.

\[d_{C} = d_{H} \int_{0}^{z} \frac{dz'}{E(z'; \Omega_{m,0}, w_0)}\]

Parameters:

z: array_like

Redshift

Returns:

comoving_distance: array_like

The comoving distance in Mpc

comoving_transverse_distance(z)

Compute the comoving distance using an analytic integral of the Pade approximation.

\[d_{C} = d_{H} \int_{0}^{z} \frac{dz'}{E(z'; \Omega_{m,0}, w_0)}\]

Parameters:

z: array_like

Redshift

Returns:

comoving_distance: array_like

The comoving distance in Mpc

comoving_volume(z)

Compute the comoving volume out to redshift z.

\[V_C = \frac{4\pi}{3} d^3_C(z; H_0, \Omega_{m,0}, w_0)\]

Parameters:

z: array_like

Redshift

Returns:

Vc: array_like

The comoving volume in \(\rm{Gpc}^3\)

dDLdz(z)

The Jacobian for the conversion of redshift to luminosity distance.

\[\frac{dd_{L}}{z} = d_C(z; H_0, \Omega_{m,0}, w_0) + (1 + z) d_{H} E(z; \Omega_{m, 0}, w0)\]

Here \(d_{C}\) is comoving distance and \(d_{H}\) is the Hubble distance.

Parameters:

z: array_like

Redshift

Returns:

dDLdz: array_like

The derivative of the luminosity distance with respect to redshift in Mpc

Notes

This function does not have a direct analog in the astropy cosmology objects, but is needed for accounting for expressing distributions of redshift as distributions over luminosity distance.

dLdH(z)

Derivative of the luminosity distance w.r.t. the Hubble distance.

\[\frac{dd_L}{dd_H} = \frac{d_L}{d_H}\]

Parameters:

z: array_like

Redshift

Returns:

array_like:

The derivative of the luminosity distance w.r.t., the Hubble distance

de_density_scale(z)

Dark energy density at redshift z.

Parameters:

z: array_like

Redshift

Returns:

rho_de: array_like

The dark energy density at redshift z

detector_to_source_frame(m1z, m2z, dL, zmin=0.0001, zmax=100)

Convert masses and luminosity distance from the detector frame to source frame masses and redshift.

This passes through the arguments to z_at_value to compute the redshift.

Parameters:

m1z: array_like

The primary mass in the detector frame

m2z: array_like

The secondary mass in the detector frame

dL: array_like

The luminosity distance in Mpc

zmin: float

The minimum redshift used in the conversion from distance to redshift, default=1e-4

zmax: float

The maximum redshift used in the conversion from distance to redshift, default=100

Returns:

m1, m2, z: array_like

The primary and secondary masses in the source frame and the redshift

differential_comoving_volume(z)

Compute the differential comoving volume element.

\[\frac{dV_{C}}{dz} = d_C^2(z; H_0, \Omega_{m,0}, w_0) d_H E(z; \Omega_{m, 0}, w_0)\]

Parameters:

z: array_like

Redshift

Returns:

dVc: array_like

The differential comoving volume element in \(\rm{Gpc}^3\)

distmod(z)

Compute the distance modulus at redshift z.

Parameters:

z: array_like

Redshift

Returns:

distmod: array_like

The distance modulus (units: mag)

efunc(z)

Compute the \(E(z)\) function for a flat wCDM cosmology.

\[E(z; \Omega_{m,0}, w_0) = \sqrt{\Omega_{m,0} (1 + z)^3 + (1 - \Omega_{m,0}) (1 + z)^{3(1 + w_0)}}\]

Parameters:

z: array_like

Redshift

Returns:

E(z): array_like

The E(z) function

property hubble_distance

Compute the Hubble distance \(D_H = c H_0^{-1}\) in Mpc.

Returns:

D_H: float

The Hubble distance in Mpc

property hubble_time

Compute the Hubble time \(t_H = H_0^{-1}\) in Gyr.

Returns:

t_H: float

The Hubble time in Gyr

inv_efunc(z)

Compute the inverse of the E(z) function for a flat wCDM cosmology.

Parameters:

z: array_like

Redshift

Returns:

inv_efunc: array_like

The inverse of the E(z) function

lookback_time(z)

Compute the lookback time using an analytic integral of the Pade approximation.

\[t_{L} = t_{H} \int_{0}^{z} \frac{dz'}{(1 + z')E(z'; \Omega_{m,0}, w_0)}\]

Parameters:

z: array_like

Redshift

Returns:

lookback_time: array_like

The lookback time in km / s / Mpc

luminosity_distance(z)

Compute the luminosity distance using an analytic integral of the Pade approximation.

\[d_L = (1 + z') d_{H} \int_{0}^{z} \frac{dz'}{E(z'; \Omega_{m,0}, w_0)}\]

Parameters:

z: array_like

Redshift

Returns:

luminosity_distance: array_like

The luminosity distance in Mpc

source_to_detector_frame(m1, m2, z)

Convert masses and redshift from the source frame to the detector frame.

Parameters:

m1: array_like

The primary mass in the source frame

m2: array_like

The secondary mass in the source frame

z: array_like

Redshift

Returns:

m1z, m2z, dL: array_like

The primary and secondary masses in the detector frame and the luminosity distance