wpwaCDM

class astropy.cosmology.wpwaCDM(H0, Om0, Ode0, wp=-1.0, wa=0.0, zp=0, Tcmb0=0, Neff=3.04, m_nu=<Quantity 0. eV>, Ob0=None, name=None)[source]

Bases: astropy.cosmology.FLRW

FLRW cosmology with a CPL dark energy equation of state, a pivot redshift, and curvature.

The equation for the dark energy equation of state uses the CPL form as described in Chevallier & Polarski Int. J. Mod. Phys. D10, 213 (2001) and Linder PRL 90, 91301 (2003), but modified to have a pivot redshift as in the findings of the Dark Energy Task Force (Albrecht et al. arXiv:0901.0721 (2009)): \(w(a) = w_p + w_a (a_p - a) = w_p + w_a( 1/(1+zp) - 1/(1+z) )\).

Parameters:
H0 : float or Quantity

Hubble constant at z = 0. If a float, must be in [km/sec/Mpc]

Om0 : float

Omega matter: density of non-relativistic matter in units of the critical density at z=0.

Ode0 : float

Omega dark energy: density of dark energy in units of the critical density at z=0.

wp : float, optional

Dark energy equation of state at the pivot redshift zp. This is pressure/density for dark energy in units where c=1.

wa : float, optional

Negative derivative of the dark energy equation of state with respect to the scale factor. A cosmological constant has wp=-1.0 and wa=0.0.

zp : float, optional

Pivot redshift – the redshift where w(z) = wp

Tcmb0 : float or scalar Quantity, optional

Temperature of the CMB z=0. If a float, must be in [K]. Default: 0 [K]. Setting this to zero will turn off both photons and neutrinos (even massive ones).

Neff : float, optional

Effective number of Neutrino species. Default 3.04.

m_nu : Quantity, optional

Mass of each neutrino species. If this is a scalar Quantity, then all neutrino species are assumed to have that mass. Otherwise, the mass of each species. The actual number of neutrino species (and hence the number of elements of m_nu if it is not scalar) must be the floor of Neff. Typically this means you should provide three neutrino masses unless you are considering something like a sterile neutrino.

Ob0 : float or None, optional

Omega baryons: density of baryonic matter in units of the critical density at z=0. If this is set to None (the default), any computation that requires its value will raise an exception.

name : str, optional

Name for this cosmological object.

Examples

>>> from astropy.cosmology import wpwaCDM
>>> cosmo = wpwaCDM(H0=70, Om0=0.3, Ode0=0.7, wp=-0.9, wa=0.2, zp=0.4)

The comoving distance in Mpc at redshift z:

>>> z = 0.5
>>> dc = cosmo.comoving_distance(z)

Attributes Summary

wa Negative derivative of dark energy equation of state w.r.t.
wp Dark energy equation of state at the pivot redshift zp
zp The pivot redshift, where w(z) = wp

Methods Summary

de_density_scale(self, z) Evaluates the redshift dependence of the dark energy density.
w(self, z) Returns dark energy equation of state at redshift z.

Attributes Documentation

wa

Negative derivative of dark energy equation of state w.r.t. a

wp

Dark energy equation of state at the pivot redshift zp

zp

The pivot redshift, where w(z) = wp

Methods Documentation

de_density_scale(self, z)[source]

Evaluates the redshift dependence of the dark energy density.

Parameters:
z : array-like

Input redshifts.

Returns:
I : ndarray, or float if input scalar

The scaling of the energy density of dark energy with redshift.

Notes

The scaling factor, I, is defined by \(\\rho(z) = \\rho_0 I\), and in this case is given by

\[ \begin{align}\begin{aligned}a_p = \frac{1}{1 + z_p}\\I = \left(1 + z\right)^{3 \left(1 + w_p + a_p w_a\right)} \exp \left(-3 w_a \frac{z}{1+z}\right)\end{aligned}\end{align} \]
w(self, z)[source]

Returns dark energy equation of state at redshift z.

Parameters:
z : array-like

Input redshifts.

Returns:
w : ndarray, or float if input scalar

The dark energy equation of state

Notes

The dark energy equation of state is defined as \(w(z) = P(z)/\rho(z)\), where \(P(z)\) is the pressure at redshift z and \(\rho(z)\) is the density at redshift z, both in units where c=1. Here this is \(w(z) = w_p + w_a (a_p - a)\) where \(a = 1/1+z\) and \(a_p = 1 / 1 + z_p\).