Flat Lambda CDM

flat_lambda_cdm ¶

Functions to compute cosmological quantities under flat lambda CDM model.

Functions¶

compute_normalized_hubble_parameter ¶

compute_normalized_hubble_parameter(redshift: Array, omega_m: Array) -> Array

Compute the normalized Hubble parameter.

Parameters:

Name	Type	Description	Default
`redshift`	`Array`	Redshift.	required
`omega_m`	`Array`	Matter density.	required

Returns:

Type	Description
`Array`	Normalized Hubble parameter.

compute_hubble_parameter ¶

compute_hubble_parameter(redshift: Array, hubble_constant: Array, omega_m: Array) -> Array

Compute the Hubble parameter.

Parameters:

Name	Type	Description	Default
`redshift`	`Array`	Redshift.	required
`hubble_constant`	`Array`	Hubble constant in km / s / Mpc.	required
`omega_m`	`Array`	Matter density.	required

Returns:

Type	Description
`Array`	Hubble parameter in km / s/ Mpc.

compute_comoving_distance ¶

compute_comoving_distance(redshift: Array, hubble_constant: Array, omega_m: Array, n_grid: int = 1000) -> Array

Compute the comoving distance.

Parameters:

Name	Type	Description	Default
`redshift`	`Array`	Redshift to evaluate the comoving distance.	required
`hubble_constant`	`Array`	Hubble constant in km / s / Mpc.	required
`omega_m`	`Array`	Matter density.	required
`n_grid`	`int`	Number of grid points to perform the numerical integration.	`1000`

Returns:

Type	Description
`Array`	Comoving distance in Mpc.

compute_differential_comoving_volume ¶

compute_differential_comoving_volume(redshift: Array, hubble_constant: Array, omega_m: Array, n_grid: int = 1000) -> Array

Compute the differential comoving volume.

Parameters:

Name	Type	Description	Default
`redshift`	`Array`	Redshift.	required
`hubble_constant`	`Array`	Hubble constant in km / s / Mpc.	required
`omega_m`	`Array`	Matter density.	required
`n_grid`	`int`	Number of grid points to perform the numerical integration.	`1000`

Returns:

Type	Description
`Array`	Differential comoving volume in Mpc^{3}.

compute_luminosity_distance ¶

compute_luminosity_distance(redshift: Array, hubble_constant: Array, omega_m: Array, n_grid: int = 1000) -> Array

Compute the luminosity distance.

Parameters:

Name	Type	Description	Default
`redshift`	`Array`	Redshift to evaluate the luminosity distance.	required
`hubble_constant`	`Array`	Hubble constant in km / s / Mpc.	required
`omega_m`	`Array`	Matter density.	required
`n_grid`	`int`	Number of grid points to perform the numerical integration.	`1000`

Returns:

Type	Description
`Array`	Luminosity distance in Mpc.

build_distance_lookup ¶

build_distance_lookup(*, hubble_constant: float = PLANCK18_H0_KM_S_MPC, omega_m: float = PLANCK18_OMEGA_M, max_redshift: float = DEFAULT_MAX_REDSHIFT, n_grid: int = DEFAULT_LOOKUP_GRID_SIZE) -> tuple[Array, Array, Array]

Build flat-ΛCDM lookup tables for redshift, comoving distance, and luminosity distance.

Parameters:

Name	Type	Description	Default
`hubble_constant`	`float`	Hubble constant in km / s / Mpc.	`PLANCK18_H0_KM_S_MPC`
`omega_m`	`float`	Matter density.	`PLANCK18_OMEGA_M`
`max_redshift`	`float`	Largest redshift tabulated by the lookup.	`DEFAULT_MAX_REDSHIFT`
`n_grid`	`int`	Number of tabulation points.	`DEFAULT_LOOKUP_GRID_SIZE`

Returns:

Type	Description
`tuple[Array, Array, Array]`	Tuple `(redshift_grid, comoving_distance_grid, luminosity_distance_grid)`.

compute_redshift_from_luminosity_distance ¶

compute_redshift_from_luminosity_distance(luminosity_distance: Array, *, hubble_constant: float = PLANCK18_H0_KM_S_MPC, omega_m: float = PLANCK18_OMEGA_M, max_redshift: float = DEFAULT_MAX_REDSHIFT, n_grid: int = DEFAULT_LOOKUP_GRID_SIZE) -> Array

Invert a luminosity distance to redshift via a flat-ΛCDM lookup table.

Parameters:

Name	Type	Description	Default
`luminosity_distance`	`Array`	Luminosity distance in Mpc.	required
`hubble_constant`	`float`	Hubble constant in km / s / Mpc.	`PLANCK18_H0_KM_S_MPC`
`omega_m`	`float`	Matter density.	`PLANCK18_OMEGA_M`
`max_redshift`	`float`	Largest redshift tabulated by the lookup.	`DEFAULT_MAX_REDSHIFT`
`n_grid`	`int`	Number of tabulation points.	`DEFAULT_LOOKUP_GRID_SIZE`

Returns:

Type	Description
`Array`	Redshift inferred from `luminosity_distance`.