Cosmology (spectroxide.cosmology)#

Flat ΛCDM background quantities, cosmology presets and the typed Cosmology dataclass. The Green’s-function and PDE-table modules pull from this module rather than redefining cosmology themselves; users can either pass a Cosmology instance or a plain dict with the same keys to anything that takes a cosmo= argument.

Quick example#

from spectroxide.cosmology import (
    Cosmology, hubble, cosmic_time, ionization_fraction,
    DEFAULT_COSMO, PLANCK2018_COSMO,
)

# Background rates with the default (Chluba 2013) parameters
H = hubble(1e5)                      # 1/s
t = cosmic_time(1e5)                 # s
X_e = ionization_fraction(1100.0)    # free electrons / H atom

# Use a typed Cosmology instance
p18 = Cosmology.planck2018()
H_p18 = hubble(1e5, p18.to_dict())

Flat ΛCDM background quantities.

Cosmology presets, the Hubble rate, photon and baryon densities, the Saha + Peebles three-level-atom recombination history, and helpers derived from them (free-electron density, baryon-photon ratio, cosmic time). The Green’s-function and PDE-table modules pull from this module rather than redefining cosmology themselves.

References

  • Peebles (1968), ApJ 153, 1.

  • Pequignot, Petitjean & Boisson (1991), A&A 251, 680 (case-B α).

  • Chluba & Thomas (2011), MNRAS 412, 748 (TLA fudge factor F = 1.125).

  • Planck Collaboration (2016), A&A 594, A13 (Planck 2015 parameters).

  • Planck Collaboration (2020), A&A 641, A6 (Planck 2018 VI parameters).

Cosmology dataclass#

Typed parameter container with class-method presets and a to_dict helper for routines that expect a plain mapping.

Cosmology

Flat ΛCDM parameters.

Cosmology.default

Chluba 2013 parameters (code default).

Cosmology.planck2015

Planck 2015 best-fit parameters.

Cosmology.planck2018

Planck 2018 best-fit parameters.

Cosmology.to_dict

Convert to a dict accepted by spectroxide.solver.solve() (cosmo=) and spectroxide.solver.run_sweep() (cosmo_params=).
class spectroxide.cosmology.Cosmology[source]#

Bases: object

Flat ΛCDM parameters. Densities are fractions Ω, not ωh².

Parameters:

  • h (float) – H₀ / (100 km/s/Mpc). Default 0.71.

  • omega_b (float) – Ω_b. Default 0.044.

  • omega_m (float) – Ω_m (total matter). Default 0.26.

  • y_p (float) – Helium mass fraction. Default 0.24.

  • t_cmb (float) – T_CMB today [K]. Default 2.726.

  • n_eff (float) – N_eff. Default 3.046.

Examples

>>> Cosmology.planck2018().h
0.6736
classmethod Cosmology.default()[source]#

Chluba 2013 parameters (code default).

classmethod Cosmology.planck2015()[source]#

Planck 2015 best-fit parameters.

classmethod Cosmology.planck2018()[source]#

Planck 2018 best-fit parameters.

Cosmology.to_dict()[source]#

Convert to a dict accepted by spectroxide.solver.solve() (cosmo=) and spectroxide.solver.run_sweep() (cosmo_params=).

Presets#

Plain-dict cosmology presets. Each contains the keys h, omega_b, omega_m, y_p, t_cmb, n_eff.

Preset

Parameters

DEFAULT_COSMO

Chluba (2013): h=0.71, Ω_b=0.044, Ω_m=0.26, Y_p=0.24, T_CMB=2.726, N_eff=3.046.

PLANCK2015_COSMO

Planck 2015 (matches CosmoTherm DI files): h=0.6727, Ω_b=0.04917, Ω_m=0.3139, Y_p=0.2467.

PLANCK2018_COSMO

Planck 2018 (Planck VI 2020, TT,TE,EE+lowE+lensing): h=0.6736, Ω_b=0.04930, Ω_m=0.3153, Y_p=0.2454.
spectroxide.cosmology.DEFAULT_COSMO = {'h': 0.71, 'n_eff': 3.046, 'omega_b': 0.044, 'omega_m': 0.26, 't_cmb': 2.726, 'y_p': 0.24}[source]#

Chluba (2013) Green’s-function paper parameters.

spectroxide.cosmology.PLANCK2015_COSMO = {'h': 0.6727, 'n_eff': 3.046, 'omega_b': 0.049169, 'omega_m': 0.313906, 't_cmb': 2.726, 'y_p': 0.2467}[source]#

Planck 2015 (Planck XIII, Table 4). T_CMB follows CosmoTherm’s DI files (Fixsen 1996 = 2.726 K), not the Planck paper value 2.7255 K — use this for CT comparisons and Cosmology.planck2015() otherwise.

spectroxide.cosmology.PLANCK2018_COSMO = {'h': 0.6736, 'n_eff': 3.044, 'omega_b': 0.0493, 'omega_m': 0.3153, 't_cmb': 2.7255, 'y_p': 0.2454}[source]#

Planck 2018 VI, Table 2 (TT,TE,EE+lowE+lensing).

Background quantities#

Flat ΛCDM Hubble rate, densities, and integrated quantities.

hubble

Hubble rate H(z) for a flat ΛCDM background.

cosmic_time

Cosmic time t(z) by quadrature of dt/dz = −1/((1+z) H(z)).

rho_gamma

Photon energy density ρ_γ(z) = (π²/15) (k_B T(z))⁴ / (ℏc)³.

omega_gamma

Present-day photon density parameter Ω_γ.

n_hydrogen

Hydrogen number density n_H(z).

n_electron

Free-electron number density n_e(z) = X_e(z) · n_H(z).

baryon_photon_ratio

Baryon-to-photon energy density ratio R(z) = 3 ρ_b / (4 ρ_γ).
spectroxide.cosmology.hubble(z, cosmo=None)[source]#

Hubble rate H(z) for a flat ΛCDM background.

\[H(z) = H_0 \sqrt{\Omega_m (1+z)^3 + \Omega_r (1+z)^4 + \Omega_\Lambda},\]

with Ω_r including the photon and N_eff neutrino contributions.

Parameters:

  • z (float or array_like) – Redshift.

  • cosmo (Mapping, optional) – Cosmological parameters. Defaults to DEFAULT_COSMO.

Returns:

float or ndarray of float64 – Hubble rate in inverse seconds (1/s).

spectroxide.cosmology.cosmic_time(z, cosmo=None, z_upper=1000000000.0, n_points=128)[source]#

Cosmic time t(z) by quadrature of dt/dz = −1/((1+z) H(z)).

Integrates from z_upper (effectively early-time t = 0) down to z using the midpoint rule in ln(1+z).

Parameters:

  • z (float) – Redshift at which to evaluate t(z).

  • cosmo (Mapping, optional) – Cosmological parameters. Defaults to DEFAULT_COSMO.

  • z_upper (float, optional) – Upper integration limit (default 1e9). Increase for very early-Universe applications (e.g., neutrino decoupling).

  • n_points (int, optional) – Number of quadrature points (default 128). Increase for higher accuracy at small z.

Returns:

float – Cosmic time in seconds (s).

spectroxide.cosmology.rho_gamma(z, cosmo=None)[source]#

Photon energy density ρ_γ(z) = (π²/15) (k_B T(z))⁴ / (ℏc)³.

Parameters:

  • z (float or array_like) – Redshift.

  • cosmo (Mapping, optional) – Cosmological parameters. Defaults to DEFAULT_COSMO.

Returns:

float or ndarray of float64 – Photon energy density in J/m³.

spectroxide.cosmology.omega_gamma(cosmo=None)[source]#

Present-day photon density parameter Ω_γ.

\[\Omega_\gamma = \rho_{\gamma,0} / \rho_{crit,0}, \qquad \rho_{\gamma,0} = \frac{\pi^2}{15} \frac{(k_B T_0)^4}{(\hbar c)^3}.\]
Parameters:

cosmo (Mapping, optional) – Cosmological parameters. Defaults to DEFAULT_COSMO.

Returns:

float – Dimensionless photon density parameter.

spectroxide.cosmology.n_hydrogen(z, cosmo=None)[source]#

Hydrogen number density n_H(z).

Computed from the baryon density assuming primordial mass fraction Y_p of helium: n_H(z) = (1 − Y_p) ρ_b(z) / m_p.

Parameters:

  • z (float or array_like) – Redshift.

  • cosmo (Mapping, optional) – Cosmological parameters. Defaults to DEFAULT_COSMO.

Returns:

float or ndarray of float64 – Number density in 1/m³.

spectroxide.cosmology.n_electron(z, cosmo=None, x_e=None)[source]#

Free-electron number density n_e(z) = X_e(z) · n_H(z).

Parameters:

  • z (float or array_like) – Redshift.

  • cosmo (Mapping, optional) – Cosmological parameters. Defaults to DEFAULT_COSMO.

  • x_e (float or array_like, optional) – Ionization fraction. If None (default), uses the cached Saha+Peebles recombination history from ionization_fraction().

Returns:

float or ndarray of float64 – Number density in 1/m³.

spectroxide.cosmology.baryon_photon_ratio(z, cosmo=None)[source]#

Baryon-to-photon energy density ratio R(z) = 3 ρ_b / (4 ρ_γ).

Used in the photon-baryon sound speed and pre-recombination perturbation theory.

Parameters:

  • z (float or array_like) – Redshift.

  • cosmo (Mapping, optional) – Cosmological parameters. Defaults to DEFAULT_COSMO.

Returns:

float or ndarray of float64 – Dimensionless baryon-to-photon energy density ratio.

Recombination#

Free-electron fraction X_e(z): Saha for helium, Peebles three-level atom for hydrogen with fudge factor F = 1.125 (Chluba & Thomas 2011). The ODE table is cached per cosmology.

ionization_fraction

Free-electron fraction X_e(z) = n_e / n_H.
spectroxide.cosmology.ionization_fraction(z, cosmo=None)[source]#

Free-electron fraction X_e(z) = n_e / n_H.

Uses Saha equilibrium for helium (He II at 54.4 eV, He I at 24.6 eV) and the Peebles three-level atom ODE for hydrogen recombination, with fudge factor F = 1.125 (Chluba & Thomas 2011). The ODE table is cached per cosmology for fast repeated lookups.

Parameters:

  • z (float or array_like) – Redshift(s).

  • cosmo (Mapping, optional) – Cosmological parameters. Defaults to DEFAULT_COSMO.

Returns:

float or ndarray of float64 – Total free-electron fraction (H + He) per hydrogen atom. Returns a Python float when z is a scalar, otherwise an array shaped like z.