# Licensed under a 3-clause BSD style license - see LICENSE.rst
from numpy import exp
import astropy.units as u
from astropy.cosmology.parameter import Parameter
from astropy.cosmology.utils import aszarr
from . import scalar_inv_efuncs
from .base import FLRW
__all__ = ["w0wzCDM"]
__doctest_requires__ = {"*": ["scipy"]}
[docs]class w0wzCDM(FLRW):
"""
FLRW cosmology with a variable dark energy equation of state and curvature.
The equation for the dark energy equation of state uses the simple form:
:math:`w(z) = w_0 + w_z z`.
This form is not recommended for z > 1.
Parameters
----------
H0 : float or scalar quantity-like ['frequency']
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.
w0 : float, optional
Dark energy equation of state at z=0. This is pressure/density for
dark energy in units where c=1.
wz : float, optional
Derivative of the dark energy equation of state with respect to z.
A cosmological constant has w0=-1.0 and wz=0.0.
Tcmb0 : float or scalar quantity-like ['temperature'], 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-like ['energy', 'mass'] or array-like, optional
Mass of each neutrino species in [eV] (mass-energy equivalency enabled).
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 or None (optional, keyword-only)
Name for this cosmological object.
meta : mapping or None (optional, keyword-only)
Metadata for the cosmology, e.g., a reference.
Examples
--------
>>> from astropy.cosmology import w0wzCDM
>>> cosmo = w0wzCDM(H0=70, Om0=0.3, Ode0=0.7, w0=-0.9, wz=0.2)
The comoving distance in Mpc at redshift z:
>>> z = 0.5
>>> dc = cosmo.comoving_distance(z)
"""
w0 = Parameter(doc="Dark energy equation of state at z=0.", fvalidate="float")
wz = Parameter(
doc="Derivative of the dark energy equation of state w.r.t. z.",
fvalidate="float",
)
def __init__(
self,
H0,
Om0,
Ode0,
w0=-1.0,
wz=0.0,
Tcmb0=0.0 * u.K,
Neff=3.04,
m_nu=0.0 * u.eV,
Ob0=None,
*,
name=None,
meta=None
):
super().__init__(
H0=H0,
Om0=Om0,
Ode0=Ode0,
Tcmb0=Tcmb0,
Neff=Neff,
m_nu=m_nu,
Ob0=Ob0,
name=name,
meta=meta,
)
self.w0 = w0
self.wz = wz
# Please see :ref:`astropy-cosmology-fast-integrals` for discussion
# about what is being done here.
if self._Tcmb0.value == 0:
self._inv_efunc_scalar = scalar_inv_efuncs.w0wzcdm_inv_efunc_norel
self._inv_efunc_scalar_args = (
self._Om0,
self._Ode0,
self._Ok0,
self._w0,
self._wz,
)
elif not self._massivenu:
self._inv_efunc_scalar = scalar_inv_efuncs.w0wzcdm_inv_efunc_nomnu
self._inv_efunc_scalar_args = (
self._Om0,
self._Ode0,
self._Ok0,
self._Ogamma0 + self._Onu0,
self._w0,
self._wz,
)
else:
self._inv_efunc_scalar = scalar_inv_efuncs.w0wzcdm_inv_efunc
self._inv_efunc_scalar_args = (
self._Om0,
self._Ode0,
self._Ok0,
self._Ogamma0,
self._neff_per_nu,
self._nmasslessnu,
self._nu_y_list,
self._w0,
self._wz,
)
[docs] def w(self, z):
r"""Returns dark energy equation of state at redshift ``z``.
Parameters
----------
z : Quantity-like ['redshift'], array-like, or `~numbers.Number`
Input redshift.
Returns
-------
w : ndarray or float
The dark energy equation of state.
Returns `float` if the input is scalar.
Notes
-----
The dark energy equation of state is defined as
:math:`w(z) = P(z)/\rho(z)`, where :math:`P(z)` is the pressure at
redshift z and :math:`\rho(z)` is the density at redshift z, both in
units where c=1. Here this is given by :math:`w(z) = w_0 + w_z z`.
"""
return self._w0 + self._wz * aszarr(z)
[docs] def de_density_scale(self, z):
r"""Evaluates the redshift dependence of the dark energy density.
Parameters
----------
z : Quantity-like ['redshift'], array-like, or `~numbers.Number`
Input redshift.
Returns
-------
I : ndarray or float
The scaling of the energy density of dark energy with redshift.
Returns `float` if the input is scalar.
Notes
-----
The scaling factor, I, is defined by :math:`\rho(z) = \rho_0 I`,
and in this case is given by
.. math::
I = \left(1 + z\right)^{3 \left(1 + w_0 - w_z\right)}
\exp \left(-3 w_z z\right)
"""
z = aszarr(z)
zp1 = z + 1.0 # (converts z [unit] -> z [dimensionless])
return zp1 ** (3.0 * (1.0 + self._w0 - self._wz)) * exp(-3.0 * self._wz * z)