# Source code for astropy.cosmology.flrw.w0wacdm

# 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, FlatFLRWMixin

__all__ = ["w0waCDM", "Flatw0waCDM"]

__doctest_requires__ = {'*': ['scipy']}

[docs]class w0waCDM(FLRW):
r"""FLRW cosmology with a CPL dark energy equation of state and curvature.

The equation for the dark energy equation of state uses the
CPL form as described in Chevallier & Polarski [1]_ and Linder [2]_:
:math:w(z) = w_0 + w_a (1-a) = w_0 + w_a z / (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.

w0 : float, optional
Dark energy equation of state at z=0 (a=1). 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 w0=-1.0 and wa=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 w0waCDM
>>> cosmo = w0waCDM(H0=70, Om0=0.3, Ode0=0.7, w0=-0.9, wa=0.2)

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.
"""

w0 = Parameter(doc="Dark energy equation of state at z=0.", fvalidate="float")
wa = Parameter(doc="Negative derivative of dark energy equation of state w.r.t. a.",
fvalidate="float")

def __init__(self, H0, Om0, Ode0, w0=-1.0, wa=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.wa = wa

# 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.w0wacdm_inv_efunc_norel
self._inv_efunc_scalar_args = (self._Om0, self._Ode0, self._Ok0,
self._w0, self._wa)
elif not self._massivenu:
self._inv_efunc_scalar = scalar_inv_efuncs.w0wacdm_inv_efunc_nomnu
self._inv_efunc_scalar_args = (self._Om0, self._Ode0, self._Ok0,
self._Ogamma0 + self._Onu0,
self._w0, self._wa)
else:
self._inv_efunc_scalar = scalar_inv_efuncs.w0wacdm_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._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_0 + w_a (1 - a) = w_0 + w_a \frac{z}{1+z}.
"""
z = aszarr(z)
return self._w0 + self._wa * z / (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::

I = \left(1 + z\right)^{3 \left(1 + w_0 + 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])
return zp1 ** (3 * (1 + self._w0 + self._wa)) * exp(-3 * self._wa * z / zp1)

[docs]class Flatw0waCDM(FlatFLRWMixin, w0waCDM):
"""FLRW cosmology with a CPL dark energy equation of state and no
curvature.

The equation for the dark energy equation of state uses the CPL form as
described in Chevallier & Polarski [1]_ and Linder [2]_:
:math:w(z) = w_0 + w_a (1-a) = w_0 + w_a z / (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.

w0 : float, optional
Dark energy equation of state at z=0 (a=1). 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 w0=-1.0 and wa=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 Flatw0waCDM
>>> cosmo = Flatw0waCDM(H0=70, Om0=0.3, w0=-0.9, wa=0.2)

The comoving distance in Mpc at redshift z:

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

To get an equivalent cosmology, but of type astropy.cosmology.w0waCDM,
use :attr:astropy.cosmology.FlatFLRWMixin.nonflat.

>>> cosmo.nonflat
w0waCDM(H0=70.0 km / (Mpc s), Om0=0.3, ...

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.
"""

def __init__(self, H0, Om0, w0=-1.0, wa=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=0.0, w0=w0, wa=wa, Tcmb0=Tcmb0,
Neff=Neff, m_nu=m_nu, Ob0=Ob0, name=name, meta=meta)

# 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.fw0wacdm_inv_efunc_norel
self._inv_efunc_scalar_args = (self._Om0, self._Ode0,
self._w0, self._wa)
elif not self._massivenu:
self._inv_efunc_scalar = scalar_inv_efuncs.fw0wacdm_inv_efunc_nomnu
self._inv_efunc_scalar_args = (self._Om0, self._Ode0,
self._Ogamma0 + self._Onu0,
self._w0, self._wa)
else:
self._inv_efunc_scalar = scalar_inv_efuncs.fw0wacdm_inv_efunc
self._inv_efunc_scalar_args = (self._Om0, self._Ode0,
self._Ogamma0, self._neff_per_nu,
self._nmasslessnu,
self._nu_y_list, self._w0,
self._wa)