StandardCosmologyWrapper

class StandardCosmologyWrapper(cosmo: FLRW)

Bases: CosmologyWrapper, NeutrinoComponent, BaryonComponent, PhotonComponent, DarkMatterComponent, MatterComponent, DarkEnergyComponent, CurvatureComponent, TotalComponent, HubbleParameter, CriticalDensity, DistanceMeasures

The Cosmology API wrapper for FLRW.

Attributes

H0	Hubble parameter at redshift 0 in km s-1 Mpc-1.
Neff	Effective number of neutrino species.
Omega_b0	Omega baryon; baryon density/critical density at z=0.
Omega_de0	Omega dark energy; dark energy density/critical density at z=0.
Omega_dm0	Omega dark matter; dark matter density/critical density at z=0.
Omega_gamma0	Omega gamma; the density/critical density of photons at z=0.
Omega_k0	Omega curvature; the effective curvature density/critical density at z=0.
Omega_m0	Omega matter; matter density/critical density at z=0.
Omega_nu0	Omega nu; the density/critical density of neutrinos at z=0.
Omega_tot0	Omega total; the total density/critical density at z=0.
T_cmb0	CMB temperature in K at z=0.
constants	The constants namespace for this cosmology object.
critical_density0	Critical density at z = 0 in Msol Mpc-3.
hubble_distance	Hubble distance in Mpc.
hubble_time	Hubble time in Gyr.
m_nu	Neutrino mass in eV.
name	The name of the cosmology instance.
scale_factor0	Scale factor at z=0.

Methods

H(z, /)	Hubble parameter \(H(z)\) in km s-1 Mpc-1.
H_over_H0(z, /)	Standardised Hubble function \(E(z) = H(z)/H_0\).
Omega_b(z, /)	Redshift-dependent baryon density parameter.
Omega_de(z, /)	Redshift-dependent dark energy density parameter.
Omega_dm(z, /)	Redshift-dependent dark matter density parameter.
Omega_gamma(z, /)	Redshift-dependent photon density parameter.
Omega_k(z, /)	Redshift-dependent curvature density parameter.
Omega_m(z, /)	Redshift-dependent non-relativistic matter density parameter.
Omega_nu(z, /)	Redshift-dependent neutrino density parameter.
Omega_tot(z, /)	Omega total; the total density/critical density at z=0.
T_cmb(z, /)	CMB temperature in K at redshift z.
age(z, /)	Age of the universe in Gyr at redshift z.
angular_diameter_distance(z1[, z2])	Angular diameter distance \(d_A(z)\) in Mpc.
comoving_distance(z1[, z2])	Comoving line-of-sight distance \(d_c(z1, z2)\) in Mpc.
comoving_volume(z1[, z2])	Comoving volume in cubic Mpc.
critical_density(z, /)	Redshift-dependent critical density in Msol Mpc-3.
differential_comoving_volume(z, /)	Differential comoving volume in cubic Mpc per steradian.
lookback_distance(z1[, z2])	Lookback distance \(d_T\) in Mpc.
lookback_time(z1[, z2])	Lookback time in Gyr.
luminosity_distance(z1[, z2])	Redshift-dependent luminosity distance \(d_L(z1, z2)\) in Mpc.
proper_distance(z1[, z2])	Proper distance \(d\) in Mpc.
proper_time(z1[, z2])	Proper time \(t\) in Gyr.
scale_factor(z, /)	Redshift-dependenct scale factor.
transverse_comoving_distance(z1[, z2])	Transverse comoving distance \(d_M(z1, z2)\) in Mpc.

__init__(cosmo: FLRW) → None

Methods

H(z, /)	Hubble parameter \(H(z)\) in km s-1 Mpc-1.
H_over_H0(z, /)	Standardised Hubble function \(E(z) = H(z)/H_0\).
Omega_b(z, /)	Redshift-dependent baryon density parameter.
Omega_de(z, /)	Redshift-dependent dark energy density parameter.
Omega_dm(z, /)	Redshift-dependent dark matter density parameter.
Omega_gamma(z, /)	Redshift-dependent photon density parameter.
Omega_k(z, /)	Redshift-dependent curvature density parameter.
Omega_m(z, /)	Redshift-dependent non-relativistic matter density parameter.
Omega_nu(z, /)	Redshift-dependent neutrino density parameter.
Omega_tot(z, /)	Omega total; the total density/critical density at z=0.
T_cmb(z, /)	CMB temperature in K at redshift z.
__init__(cosmo)
age(z, /)	Age of the universe in Gyr at redshift z.
angular_diameter_distance(z1[, z2])	Angular diameter distance \(d_A(z)\) in Mpc.
comoving_distance(z1[, z2])	Comoving line-of-sight distance \(d_c(z1, z2)\) in Mpc.
comoving_volume(z1[, z2])	Comoving volume in cubic Mpc.
critical_density(z, /)	Redshift-dependent critical density in Msol Mpc-3.
differential_comoving_volume(z, /)	Differential comoving volume in cubic Mpc per steradian.
lookback_distance(z1[, z2])	Lookback distance \(d_T\) in Mpc.
lookback_time(z1[, z2])	Lookback time in Gyr.
luminosity_distance(z1[, z2])	Redshift-dependent luminosity distance \(d_L(z1, z2)\) in Mpc.
proper_distance(z1[, z2])	Proper distance \(d\) in Mpc.
proper_time(z1[, z2])	Proper time \(t\) in Gyr.
scale_factor(z, /)	Redshift-dependenct scale factor.
transverse_comoving_distance(z1[, z2])	Transverse comoving distance \(d_M(z1, z2)\) in Mpc.

Attributes

H0	Hubble parameter at redshift 0 in km s-1 Mpc-1.
Neff	Effective number of neutrino species.
Omega_b0	Omega baryon; baryon density/critical density at z=0.
Omega_de0	Omega dark energy; dark energy density/critical density at z=0.
Omega_dm0	Omega dark matter; dark matter density/critical density at z=0.
Omega_gamma0	Omega gamma; the density/critical density of photons at z=0.
Omega_k0	Omega curvature; the effective curvature density/critical density at z=0.
Omega_m0	Omega matter; matter density/critical density at z=0.
Omega_nu0	Omega nu; the density/critical density of neutrinos at z=0.
Omega_tot0	Omega total; the total density/critical density at z=0.
T_cmb0	CMB temperature in K at z=0.
constants	The constants namespace for this cosmology object.
critical_density0	Critical density at z = 0 in Msol Mpc-3.
hubble_distance	Hubble distance in Mpc.
hubble_time	Hubble time in Gyr.
m_nu	Neutrino mass in eV.
name	The name of the cosmology instance.
scale_factor0	Scale factor at z=0.
cosmo	The underlying FLRW instance.

H(z: Quantity | NDFloating | float, /) → Quantity

Hubble parameter \(H(z)\) in km s-1 Mpc-1.

Parameters:

zArray

The redshift(s) at which to evaluate the Hubble parameter.

Returns:

Array

property H0: Quantity

Hubble parameter at redshift 0 in km s-1 Mpc-1.

H_over_H0(z: Quantity | NDFloating | float, /) → Quantity

Standardised Hubble function \(E(z) = H(z)/H_0\).

Parameters:

zArray

The redshift(s) at which to evaluate.

Returns:

Array

property Neff: Quantity

Effective number of neutrino species.

Omega_b(z: InputT, /) → Quantity

Redshift-dependent baryon density parameter.

Parameters:

zArray, positional-only

Input redshift.

Returns:

Array

property Omega_b0: Quantity

Omega baryon; baryon density/critical density at z=0.

Omega_de(z: InputT, /) → Quantity

Redshift-dependent dark energy density parameter.

Parameters:

zArray, positional-only

Input redshift.

Returns:

Array

property Omega_de0: Quantity

Omega dark energy; dark energy density/critical density at z=0.

Omega_dm(z: InputT, /) → Quantity

Redshift-dependent dark matter density parameter.

Parameters:

zArray, positional-only

Input redshift.

Returns:

Array

Notes

This does not include neutrinos, even if non-relativistic at the redshift of interest.

property Omega_dm0: Quantity

Omega dark matter; dark matter density/critical density at z=0.

Omega_gamma(z: InputT, /) → Quantity

Redshift-dependent photon density parameter.

Parameters:

zArray, positional-only

Input redshift.

Returns:

Array

property Omega_gamma0: Quantity

Omega gamma; the density/critical density of photons at z=0.

Omega_k(z: InputT, /) → Quantity

Redshift-dependent curvature density parameter.

Parameters:

zArray, positional-only

Input redshift.

Returns:

Array

property Omega_k0: Quantity

Omega curvature; the effective curvature density/critical density at z=0.

Omega_m(z: InputT, /) → Quantity

Redshift-dependent non-relativistic matter density parameter.

Parameters:

zArray, positional-only

Input redshift.

Returns:

Array

Notes

This does not include neutrinos, even if non-relativistic at the redshift of interest; see Omega_nu.

property Omega_m0: Quantity

Omega matter; matter density/critical density at z=0.

Omega_nu(z: InputT, /) → Quantity

Redshift-dependent neutrino density parameter.

Parameters:

zArray, positional-only

Input redshift.

Returns:

Array

property Omega_nu0: Quantity

Omega nu; the density/critical density of neutrinos at z=0.

Omega_tot(z: InputT, /) → Quantity

Omega total; the total density/critical density at z=0.

property Omega_tot0: Quantity

Omega total; the total density/critical density at z=0.

T_cmb(z: InputT, /) → Quantity

CMB temperature in K at redshift z.

Parameters:

zQuantity, positional-only

Input redshift.

Returns:

Quantity

property T_cmb0: Quantity

CMB temperature in K at z=0.

age(z: InputT, /) → Quantity

Age of the universe in Gyr at redshift z.

Parameters:

zQuantity

Input redshift.

Returns:

Quantity

angular_diameter_distance(z1: InputT, z2: InputT | None = None, /) → Quantity

Angular diameter distance \(d_A(z)\) in Mpc.

This gives the proper (sometimes called ‘physical’) transverse distance corresponding to an angle of 1 radian for an object at redshift z ([1], [2], [3]).

Parameters:

zQuantity, positional-only

z1, z2Quantity, positional-only

Input redshifts. If one argument z is given, the distance \(d_A(0, z)\) is returned. If two arguments z1, z2 are given, the distance \(d_A(z_1, z_2)\) is returned.

Returns:

Quantity

References

[1]

Weinberg, 1972, pp 420-424; Weedman, 1986, pp 421-424.

[2]

Weedman, D. (1986). Quasar astronomy, pp 65-67.

[3]

Peebles, P. (1993). Principles of Physical Cosmology, pp 325-327.

comoving_distance(z1: InputT, z2: InputT | None = None, /) → Quantity

Comoving line-of-sight distance \(d_c(z1, z2)\) in Mpc.

The comoving distance along the line-of-sight between two objects remains constant with time for objects in the Hubble flow.

Parameters:

zQuantity, positional-only

z1, z2Quantity, positional-only

Input redshifts. If one argument z is given, the time \(t_T(0, z)\) is returned. If two arguments z1, z2 are given, the time \(t_T(z_1, z_2)\) is returned.

Returns:

Quantity

comoving_volume(z1: InputT, z2: InputT | None = None, /) → Quantity

Comoving volume in cubic Mpc.

This is the volume of the universe encompassed by redshifts less than z. For the case of \(\Omega_k = 0\) it is a sphere of radius comoving_distance but it is less intuitive if \(\Omega_k\) is not.

Parameters:

zQuantity, positional-only

z1, z2Quantity, positional-only

Input redshifts. If one argument z is given, the volume \(V_c(0, z)\) is returned. If two arguments z1, z2 are given, the volume \(V_c(z_1, z_2)\) is returned.

Returns:

Quantity

property constants: CosmologyConstantsNamespace

The constants namespace for this cosmology object.

cosmo: FLRW

The underlying FLRW instance.

critical_density(z: Quantity | NDFloating | float, /) → Quantity

Redshift-dependent critical density in Msol Mpc-3.

property critical_density0: Quantity

Critical density at z = 0 in Msol Mpc-3.

differential_comoving_volume(z: InputT, /) → Quantity

Differential comoving volume in cubic Mpc per steradian.

If \(V_c\) is the comoving volume of a redshift slice with solid angle \(\Omega\), this function returns

\[\mathtt{differential\_comoving\_volume(z)} = \frac{dV_c}{d\Omega \, dz} = \frac{c \, d_M^2(z)}{H(z)} \;.\]

Parameters:

zQuantity, positional-only

Input redshift

Returns:

Quantity

The differential comoving volume \(dV_c\) in Mpc3 sr-1.

property hubble_distance: Quantity

Hubble distance in Mpc.

property hubble_time: Quantity

Hubble time in Gyr.

lookback_distance(z1: InputT, z2: InputT | None = None, /) → Quantity

Lookback distance \(d_T\) in Mpc.

The lookback distance is the subjective distance it took light to travel from redshift z1 to z2.

Parameters:

zQuantity, positional-only

z1, z2Quantity, positional-only

Input redshifts. If one argument z is given, the distance \(d_T(0, z)\) is returned. If two arguments z1, z2 are given, the distance \(d_T(z_1, z_2)\) is returned.

Returns:

Quantity

The lookback distance \(d_T\) in Mpc.

lookback_time(z1: InputT, z2: InputT | None = None, /) → Quantity

Lookback time in Gyr.

The lookback time is the time that it took light from being emitted at one redshift to being observed at another redshift. Effectively it is the difference between the age of the Universe at the two redshifts.

Parameters:

zQuantity, positional-only

z1, z2Quantity, positional-only

Input redshifts. If one argument z is given, the time \(t_T(0, z)\) is returned. If two arguments z1, z2 are given, the time \(t_T(z_1, z_2)\) is returned.

Returns:

Quantity

luminosity_distance(z1: InputT, z2: InputT | None = None, /) → Quantity

Redshift-dependent luminosity distance \(d_L(z1, z2)\) in Mpc.

This is the distance to use when converting between the bolometric flux from an object at redshift z and its bolometric luminosity [1].

Parameters:

zQuantity, positional-only

z1, z2Quantity, positional-only

Input redshifts. If one argument z is given, the distance \(d_L(0, z)\) is returned. If two arguments z1, z2 are given, the distance \(d_L(z_1, z_2)\) is returned.

Returns:

Quantity

References

[1]

Weinberg, 1972, pp 420-424; Weedman, 1986, pp 60-62.

property m_nu: tuple[Quantity, ...]

Neutrino mass in eV.

property name: str | None

The name of the cosmology instance.

proper_distance(z1: InputT, z2: InputT | None = None, /) → Quantity

Proper distance \(d\) in Mpc.

The proper distance is the distance between two objects at redshifts z1 and z2, including the effects of the expansion of the universe.

Parameters:

zQuantity, positional-only

z1, z2Quantity, positional-only

Input redshifts. If one argument z is given, the distance \(d(0, z)\) is returned. If two arguments z1, z2 are given, the distance \(d(z_1, z_2)\) is returned.

Returns:

Quantity

The proper distance \(d\) in Mpc.

proper_time(z1: InputT, z2: InputT | None = None, /) → Quantity

Proper time \(t\) in Gyr.

The proper time is the proper distance divided by c.

Parameters:

zQuantity, positional-only

z1, z2Quantity, positional-only

Input redshifts. If one argument z is given, the time \(t(0, z)\) is returned. If two arguments z1, z2 are given, the time \(t(z_1, z_2)\) is returned.

Returns:

Quantity

The proper time \(t\) in Gyr.

scale_factor(z: InputT, /) → Quantity

Redshift-dependenct scale factor.

The scale factor is defined as \(a = a_0 / (1 + z)\).

Parameters:

zQuantity or float, positional-only

The redshift(s) at which to evaluate the scale factor.

Returns:

Quantity

property scale_factor0: Quantity

Scale factor at z=0.

transverse_comoving_distance(z1: InputT, z2: InputT | None = None, /) → Quantity

Transverse comoving distance \(d_M(z1, z2)\) in Mpc.

This value is the transverse comoving distance at redshift z corresponding to an angular separation of 1 radian. This is the same as the comoving distance if \(\Omega_k\) is zero (as in the current concordance Lambda-CDM model).

Parameters:

zQuantity, positional-only

z1, z2Quantity, positional-only

Input redshifts. If one argument z is given, the time \(d_M(0, z)\) is returned. If two arguments z1, z2 are given, the time \(d_M(z_1, z_2)\) is returned.

Returns:

Quantity