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.

The redshift grid is 0 followed by n_grid - 1 points spaced uniformly in log z from MIN_LOOKUP_NONZERO_REDSHIFT to max_redshift. A grid uniform in z would leave a first interval so wide that linear interpolation misstates d_L there by about (1 - q0) / 2 * dz; the logarithmic grid keeps the relative interpolation error small down to MIN_LOOKUP_NONZERO_REDSHIFT.

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)`.

interpolate_within_lookup ¶

interpolate_within_lookup(values: Array, grid: Array, table: Array, name: str) -> Array

Linearly interpolate table over grid at values, refusing to extrapolate.

Interpolating outside [0, grid[-1]] would silently return the table edge. Concrete (eager) input outside that range raises ValueError. Traced input (under jax.jit, jax.vmap, jax.lax.scan, ...) cannot raise on a data-dependent condition, so there each out-of-range element is returned as NaN instead; it does not raise. In-range elements are unaffected either way.

Parameters:

Name	Type	Description	Default
`values`	`Array`	Values to be looked up.	required
`grid`	`Array`	Increasing tabulation points, starting at 0.	required
`table`	`Array`	Tabulated values at `grid`.	required
`name`	`str`	Name of the looked-up quantity, used in the error message.	required

Returns:

Type	Description
`Array`	Interpolated values, NaN where a traced value is out of range.

Raises:

Type	Description
`ValueError`	If concrete `values` contain an element below 0 or above `grid[-1]`.

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`.

Raises:

Type	Description
`ValueError`	If any concrete distance lies outside `[0, d_L(max_redshift)]`. Traced out-of-range distances are returned as NaN instead; see :func:`interpolate_within_lookup`.