Carroll1992¶

class hmf.cosmology.growth_factor.Carroll1992(*args, **kwargs)[source]¶

Analytic approximation for the growth factor from Carroll et al. 1992.

This formula is based on a formula in Lahav+1991 and Schechter and Lightman 1991.

This formula is explicitly only valid at z=0, and a warning will be raised if you try to use it at z>0. However, the formula is actually pretty accurate at non-zero redshifts if redshift-dependent values for Omega_m and Omega_L are used.

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.