StandardCosmologyWrapper¶

class StandardCosmologyWrapper(cosmo: FLRW)[source]¶

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.
`inv_comoving_distance`(dc, /)	Redshift at a given comoving line-of-sight distance.
`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.
`inv_comoving_distance`(dc, /)	Redshift at a given comoving line-of-sight distance.
`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.

inv_comoving_distance(dc: InputT, /) → Array¶

Redshift at a given comoving line-of-sight distance.

The redshift at a comoving distance along the line-of-sight between two objects.

Parameters:

dcArray, positional-only: The comoving line-of-sight distance \(d_c\) in Mpc.

Returns:

Array: The redshift at a given comoving line-of-sight distance.

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