mycosmo.cosmology module

Cosmology.

This module implements various cosmology routines.

mycosmo.cosmology.critical_density(redshift: float | ndarray, cosmo_dict: dict[str, float]) → float | ndarray

Critical Density.

Calculate the critical density at a given redshift using the cosmological parameter values provided.

Parameters:

redshiftfloat or numpy.ndarray

Redshift(s) at which the critical density should be calculated

cosmo_dictdict

Dictionary of cosmological constants. Must contain the following keys:

• H0: The Hubble parameter value at redshift zero.

• omega_m_0: The matter density at redshift zero.

• omega_k_0: The curvature density at redshift zero.

• omega_lambda_0: The dark energy density at redshift zero.

Returns:

float or numpy.ndarray

Value of the critical density (km/m^3) at the specified redshift(s) for a given cosmology.

Notes

This function implements the calculation of the critical density as follows:

\[\rho_c(z) = \frac{3H^2(z)}{8\pi G}\]

Examples

>>> from mycosmo.cosmology import critical_density
>>> cosmo_dict = {
...     "H0": 70,
...     "omega_m_0": 0.3,
...     "omega_k_0": 0.0,
...     "omega_lambda_0": 0.7,
... }
>>> float(critical_density(0.0, cosmo_dict))
9.203859495267889e-27

mycosmo.cosmology.hubble(redshift: float | ndarray, cosmo_dict: dict[str, float]) → float | ndarray

Hubble Parameter.

Calculate the Hubble parameter at a given redshift using the cosmological parameter values provided.

Parameters:

redshiftfloat or numpy.ndarray

Redshift(s) at which the Hubble parameter should be calculated

cosmo_dictdict

Dictionary of cosmological constants. Must contain the following keys:

• H0: The Hubble parameter value at redshift zero.

• omega_m_0: The matter density at redshift zero.

• omega_k_0: The curvature density at redshift zero.

• omega_lambda_0: The dark energy density at redshift zero.

Returns:

float or numpy.ndarray

Value of the Hubble parameter (km/s/Mpc) at the specified redshift(s) for a given cosmology.

Notes

This function implements the calculation of the Hubble parameter as follows:

\[H(z) = \sqrt{H_0^2 (\Omega_{m,0}(1+z)^3 + \Omega_{k,0}(1+z)^2 + \Omega_{\Lambda,0})}\]

Examples

>>> from mycosmo.cosmology import hubble
>>> cosmo_dict = {
...     "H0": 70,
...     "omega_m_0": 0.3,
...     "omega_k_0": 0.0,
...     "omega_lambda_0": 0.7,
... }
>>> float(hubble(0.0, cosmo_dict))
70.0