Module constants

Physical and cosmological constants in SI units.

All values from CODATA 2018 / Particle Data Group unless noted.

Grouped as:

• Fundamental: C_LIGHT, HBAR, HPLANCK, K_BOLTZMANN, M_ELECTRON, M_PROTON, SIGMA_THOMSON, ALPHA_FS — feed Compton scattering rates, Planck normalisations, and DC/BR emission prefactors.
• Unit conversions: EV_IN_JOULES, MPC_IN_METERS.
• Atomic physics: E_RYDBERG_*, E_HE_*, LAMBDA_LYA, LAMBDA_2S1S — used by crate::recombination for the Peebles 3-level atom.
• Derived: LAMBDA_ELECTRON, M_E_C2, M_E_C2_EV.
• Cosmology: T_CMB_0, Y_P, N_EFF, and Planck spectral integrals (G1_PLANCK = π²/6, G2_PLANCK = 2ζ(3), G3_PLANCK = π⁴/15, I4_PLANCK = 4 G₃), plus the derived μ-channel coefficients BETA_MU, KAPPA_C, ALPHA_RHO, and the era-boundary redshifts Z_MU (μ-distortion freeze-out) and Z_MU_Y (μ→y transition). These are used by both the PDE solver and the Green’s-function visibility functions.

Constants

ALPHA_FS

ALPHA_MU

α_μ = 1/β_μ = π²/(18ζ(3)) — relates μ to energy

ALPHA_RHO

α_ρ = G₂/G₃ — ratio of photon number to energy spectral integrals.

BETA_MU

β_μ = 3ζ(3)/ζ(2) ≈ 2.1923 — frequency of μ-distortion zero crossing

C_LIGHT

EV_IN_JOULES

1 eV in Joules (exact by 2019 SI redefinition)

E_HE_II_ION_EV

He²⁺ ionization energy (He II → He I), in eV.

E_HE_I_ION_EV

He⁺ ionization energy (He I → He), in eV.

E_ION_N2

Ionization energy from n=2 level (E_Rydberg / 4), in J.

E_RYDBERG

Hydrogen ionization energy, in J.

E_RYDBERG_EV

Hydrogen ionization energy (1s ground state), in eV.

F_HE

Helium number fraction relative to hydrogen: f_He = Y_p / (4*(1-Y_p))

G1_PLANCK

G_1 = ∫₀^∞ x n_pl(x) dx = π²/6 = ζ(2)

G2_PLANCK

G_2 = ∫₀^∞ x² n_pl(x) dx = 2ζ(3)

G3_PLANCK

G_3 = ∫₀^∞ x³ n_pl(x) dx = π⁴/15

G_NEWTON

HBAR

HPLANCK

I4_PLANCK

I_4 = ∫₀^∞ x⁴ n_pl (1+n_pl) dx = 4π⁴/15

KAPPA_C

κ_c = 3 ∫x³ M(x) dx / G₃ = 12/β_μ − 9G₂/G₃ ≈ 2.1419

KAPPA_GAMMA

κ_γ = 8π / λ_e³ — photon phase space density prefactor.

KM_PER_MPC

km/s/Mpc → 1/s

K_BOLTZMANN

LAMBDA_2S1S

2s→1s two-photon decay rate [s⁻¹]

LAMBDA_ELECTRON

Electron Compton wavelength: h / (m_e * c)

LAMBDA_LYA

Lyman-alpha wavelength, in m.

MPC_IN_METERS

1 Mpc in meters

M_ELECTRON

M_E_C2

m_e c^2 in Joules

M_E_C2_EV

m_e c^2 in eV

M_PROTON

N_EFF

Effective number of neutrino species

SIGMA_THOMSON

T_CMB_0

Default CMB temperature today, in K.

X_BALANCED

x₀ = 4/(3α_ρ) ≈ 3.60 — balanced injection frequency.

Y_P

Helium mass fraction

ZETA_3

Riemann zeta function ζ(3) = 1.202…

Z_MU

μ-era thermalization redshift (Chluba 2013, MNRAS 436, 2232)

Z_MU_Y

μ-y transition redshift