Background cosmology and species

The homogeneous universe in Cosmic.jl is a Cosmology: a container of species, each knowing its own energy density $\rho(a)/\rho_{c,0}$ and equation of state $w(a)$. The Friedmann equation is then just the sum

\[\frac{H^2(a)}{H_0^2} = \sum_i \frac{\rho_i(a)}{\rho_{c,0}},\]

and every background quantity — distances, ages, horizons — is an integral over it. Nothing assumes a particular species content, so exotic components (warm or decaying dark matter, quintessence) enter on exactly the same footing as photons and baryons.

Building a cosmology

cosmology() assembles the species from familiar parameters. Two choices are worth spelling out. First, the helium fraction defaults to Yp = :bbn: given $\omega_b$ and $N_{\rm eff}$, nucleosynthesis fixes $Y_p$, so treating it as a free parameter would let a model quietly carry a helium abundance inconsistent with its own baryon density; the network is solved (and cached) instead. Second, dark energy closes the budget: $\Omega_{\rm DE}$ is never an input but whatever flatness (or the requested $\Omega_k$) demands.

Massive neutrinos are never approximated by a power law in $a$. Their density comes from the exact phase-space integral $\rho \propto \int dq\, q^2 \sqrt{q^2 + (ma/T_{\nu,0})^2}\, f_0(q)$, which crosses from radiation-like to matter-like behaviour with no interpolation.

Dark energy

Four options, in increasing generality:

a cosmological constant (the default, w0 = -1, wa = 0);
the CPL fluid w(a) = w0 + wa (1 - a);
an arbitrary w_func(a), whose density integrates the continuity equation numerically;
a quintessence field: pass a potential V_scf (in units of the critical density, with the field in reduced Planck masses) and its derivative dV_scf. The Klein–Gordon equation is solved through the full expansion history, with the potential amplitude shot by bisection so the field's density today closes the budget exactly. The field starts frozen — the early-time attractor under Hubble friction — and its $w(a)$ is whatever the potential produces, not a parameterization.

For anything other than the cosmological constant, the corresponding perturbations are evolved automatically (see Linear perturbations); a true $\Lambda$ carries none, exactly.

Dark matter beyond CDM

Warm dark matter (cosmology(m_wdm = ..., Ω_wdm = ...)) is a thermal fermion relic riding the same momentum-resolved machinery as massive neutrinos. Its temperature ratio to the neutrinos follows from the abundance through the exact phase-space integral rather than the usual $93.14\,\mathrm{eV}$ shortcut (which assumes instantaneous-decoupling neutrino temperature and is about 1% off). The free-streaming suppression of structure it produces is computed, not fitted; the resulting cutoff reproduces the Viel transfer function at the few-percent level as an output.

Decaying dark matter (Γ_dcdm in km/s/Mpc, Ω_dcdm_ini the abundance it would have today without decay) converts to a dark radiation component through $\dot\rho_{\rm dcdm} = -3\mathcal{H}\rho_{\rm dcdm} - a\Gamma\rho_{\rm dcdm}$. No closed form exists — the decay is in proper time, so the history depends on the expansion it modifies — and the coupled system is solved at construction, self-consistently with the dark-energy closure. The realised $\Omega_{\rm dcdm}$ today matches the analytic $\Omega_{\rm ini} e^{-\Gamma t_0}$ to five digits, and the full perturbation sector (including the sourced dark-radiation hierarchy) reproduces the decay response of CLASS to better than half a percent in the CMB.

Annihilating dark matter affects the thermal history rather than the background; see Thermal history.

Distances and times

The usual kinematic toolbox — comoving, transverse comoving, angular-diameter and luminosity distances, lookback time, age, conformal time — all as direct integrals over $E(a)$ with curvature handled exactly in open, flat, and closed geometries.

Reference

Cosmic.Cosmology — Type

Cosmology

Container for a background model. Build one with cosmology rather than calling this constructor directly.

Fields beyond the species list:

h : H0 = 100h km/s/Mpc
Tcmb : CMB temperature today, K
Yp : primordial helium mass fraction (needed by recombination)
A_s,n_s,k_pivot : primordial curvature power spectrum, PR(k) = As (k/kpivot)^(ns - 1)