# Licensed under a 3-clause BSD style license - see LICENSE.rst
from numpy import exp
import astropy.units as u
from astropy.cosmology import units as cu
from astropy.cosmology.parameter import Parameter
from astropy.cosmology.utils import aszarr
from . import scalar_inv_efuncs
from .base import FLRW
__all__ = ["wpwaCDM"]
__doctest_requires__ = {"*": ["scipy"]}
[docs]class wpwaCDM(FLRW):
r"""
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 [1]_ and Linder [2]_, but modified to
have a pivot redshift as in the findings of the Dark Energy Task Force
[3]_: :math:`w(a) = w_p + w_a (a_p - a) = w_p + w_a( 1/(1+zp) - 1/(1+z) )`.
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.
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 or quantity-like ['redshift'], optional
Pivot redshift -- the redshift where w(z) = wp
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 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)
References
----------
.. [1] Chevallier, M., & Polarski, D. (2001). Accelerating Universes with
Scaling Dark Matter. International Journal of Modern Physics D,
10(2), 213-223.
.. [2] Linder, E. (2003). Exploring the Expansion History of the
Universe. Phys. Rev. Lett., 90, 091301.
.. [3] Albrecht, A., Amendola, L., Bernstein, G., Clowe, D., Eisenstein,
D., Guzzo, L., Hirata, C., Huterer, D., Kirshner, R., Kolb, E., &
Nichol, R. (2009). Findings of the Joint Dark Energy Mission Figure
of Merit Science Working Group. arXiv e-prints, arXiv:0901.0721.
"""
wp = Parameter(
doc="Dark energy equation of state at the pivot redshift zp.", fvalidate="float"
)
wa = Parameter(
doc="Negative derivative of dark energy equation of state w.r.t. a.",
fvalidate="float",
)
zp = Parameter(doc="The pivot redshift, where w(z) = wp.", unit=cu.redshift)
def __init__(
self,
H0,
Om0,
Ode0,
wp=-1.0,
wa=0.0,
zp=0.0 * cu.redshift,
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.wp = wp
self.wa = wa
self.zp = zp
# Please see :ref:`astropy-cosmology-fast-integrals` for discussion
# about what is being done here.
apiv = 1.0 / (1.0 + self._zp.value)
if self._Tcmb0.value == 0:
self._inv_efunc_scalar = scalar_inv_efuncs.wpwacdm_inv_efunc_norel
self._inv_efunc_scalar_args = (
self._Om0,
self._Ode0,
self._Ok0,
self._wp,
apiv,
self._wa,
)
elif not self._massivenu:
self._inv_efunc_scalar = scalar_inv_efuncs.wpwacdm_inv_efunc_nomnu
self._inv_efunc_scalar_args = (
self._Om0,
self._Ode0,
self._Ok0,
self._Ogamma0 + self._Onu0,
self._wp,
apiv,
self._wa,
)
else:
self._inv_efunc_scalar = scalar_inv_efuncs.wpwacdm_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._wp,
apiv,
self._wa,
)
[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 :math:`w(z) = w_p + w_a (a_p - a)` where
:math:`a = 1/1+z` and :math:`a_p = 1 / 1 + z_p`.
"""
apiv = 1.0 / (1.0 + self._zp.value)
return self._wp + self._wa * (apiv - 1.0 / (aszarr(z) + 1.0))
[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::
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)
"""
z = aszarr(z)
zp1 = z + 1.0 # (converts z [unit] -> z [dimensionless])
apiv = 1.0 / (1.0 + self._zp.value)
return zp1 ** (3.0 * (1.0 + self._wp + apiv * self._wa)) * exp(
-3.0 * self._wa * z / zp1
)