GrowthFactor

class hmf.cosmology.growth_factor.GrowthFactor(*args, **kwargs)

Growth factor calculation that intelligently chooses which method to use.

This class chooses which growth factor calculation to use based on the cosmology and the parameters. It prioritises first accuracy, then performance, conditional on the parameters. In particular, it uses the following logic to compute the growth factor:

• If the dark energy equation of state is not w = -1, use the ODE solution; otherwise

• If the cosmology has no radiation component, or the redshift is low enough such that the radiation component can be neglected: - If the cosmology is flat, use analytic forms of Eisenstein 1997 - Otherwise, use the integral form defined in Heath 1977.

• Otherwise, solve the full ODE numerically (also presented in the docs).

Attributes

Or0	The fractional radiation density at redshift zero.
references	References to cite when this model is used, each a formatted citation string.

Methods

dlne_dlna(z)

Compute the derivative of ln(E(a)) with respect to ln(a).

This is useful for the growth factor, which has terms \(E'(a)/E(a) \equiv (1/a)*dlnE/dlna\) in its definition.

This implementation simply uses the exact definition from astropy of E(a) and writes down the derivative analytically. The dark-energy density scales as \(\rho_{\rm DE}(a) \propto \exp(-3\int (1+w)\, d\ln a)\), so its logarithmic derivative is \(-3(1+w(a))\), which vanishes only for a cosmological constant. With massive neutrinos, the radiation term is \(\Omega_\gamma (1 + N(z)) a^{-4}\), where \(N(z)\) is astropy’s nu_relative_density. \(N\) varies with time as the neutrinos become non-relativistic, so its derivative is included, computed by central finite difference in \(\ln(1+z)\).

classmethod get_models() → Mapping[str, type]

Get a read-only mapping of all implemented models for this component.

The mapping is a live view of the registry, so it shows models registered later, but it can not be used to add or remove models.

growth_factor(z)

Compute the normalized growth factor, \(D(a) = D^+(a)/D^+(a=1)\).

Parameters:

z (array_like) – Redshift.

Returns:

gf – The growth factor at z.

Return type:

array_like

growth_rate(z) → float | ndarray

Compute the growth rate, \(f(a) = d\ln D^+ / d\ln a\).

Parameters:

z (array_like) – Redshift.

Returns:

gr – The growth rate at z.

Return type:

array_like

radiation_density(z)

The fractional radiation density as a function of redshift.