Cosmic.jl

Cosmic.jl is a cosmology code in pure Julia: a Boltzmann solver in the tradition of CLASS and CAMB, together with the early-universe machinery those codes outsource — Big Bang nucleosynthesis, neutrino decoupling, CMB spectral distortions — solved within the same package and the same conventions.

The guiding principle is exactness. Wherever a standard code would switch to a fitting formula or a truncated expansion, Cosmic.jl either integrates the exact expression or documents precisely what is cached and how it was generated. Every physics module is cross-checked against an independent reference (CLASS, CAMB, FAST-PT, or published closed forms) before it is trusted; the numbers quoted below come from those comparisons.

What it computes

The homogeneous universe: any mixture of photons, baryons, cold dark matter, massless and massive neutrinos (with chemical potentials or arbitrary distribution functions), warm dark matter, decaying dark matter, spatial curvature, and dark energy as a cosmological constant, a $w_0$–$w_a$ fluid, an arbitrary $w(a)$, or a quintessence field rolling in a user-supplied potential. Distances, ages, horizons, and the BBN abundances follow from the one cosmology(...) object.

Recombination through a port of HyRec (effective multi-level atom), with reionization, exotic energy injection from annihilating or decaying dark matter, and the derived quantities of CMB analysis: optical depths, visibility, the sound horizon, $z_*$, $z_{\rm drag}$, $\theta_*$.

The linear perturbations: a stiff-integrated Boltzmann hierarchy in the conformal Newtonian gauge (no tight-coupling approximation) with momentum-resolved massive neutrinos, adiabatic and all four regular isocurvature initial conditions, decaying-dark-matter and dark-energy perturbation sectors, and tensor modes — in flat, open, and closed geometries. CMB temperature and polarization agree with CLASS at the 0.3% level; the lensed spectra (computed by the exact correlation-function method) at 0.3–0.4% with $C_\ell^{\phi\phi}$ to better than 1%.

The matter power spectrum, linear and nonlinear: halofit (0.25% against CLASS), HMcode-2020 (sub-percent against CAMB to $k = 1\,h$/Mpc), and the exact 1-loop EFT of large-scale structure with IR resummation, whose loop integrals match the independent FFTLog code FAST-PT to better than 0.5%.

The primordial universe: power-law, arbitrary, or multi-field-correlated primordial spectra; an inflaton module that integrates the exact Mukhanov–Sasaki equation for any potential $V(\phi)$ (with an optional effective sound speed $c_s(N)$); and the scalar-induced gravitational-wave background from the Kohri–Terada kernel, validated against its published closed forms.

CMB spectral distortions: the thermalization Green's function with exact double-Compton and Karzas–Latter free–free coefficients, and $\mu$, $y$ amplitudes from any injection history.

Installation

Cosmic requires Julia 1.9+:

pkg> add https://github.com/aburousan/Cosmic.jl

Quick start

using Cosmic

c   = cosmology()                          # Planck-2018-like defaults, Yp from BBN
rec = recombination(c)                     # HyRec thermal history
cl  = cmb_spectra(c, rec; lmax = 2500)     # unlensed TT/TE/EE
len = lensed_cmb_spectra(c, rec)           # lensed spectra + Cℓ^φφ
P   = matter_power_spectrum(c, rec; z = 0) # linear P(k)
hm  = hmcode_power(P)                      # nonlinear P(k)

A feature spectrum from an inflaton potential, and its induced gravitational waves:

V(φ)  = 0.5 * 6e-6^2 * φ^2
dV(φ) = 6e-6^2 * φ
s  = inflaton_spectrum(V, dV; φ0 = 16.0, N_pivot = 55)
c  = cosmology(primordial = s)             # the computed spectrum feeds everything
gw = sigw_spectrum(s, c; kmin = 1e4, kmax = 1e9)
sigw_ΔNeff(gw, c)                          # the integrated N_eff of the background

Examples live in the Examples folder.

Documentation map

Contributing

Open an issue or pull request on the GitHub page. New features should come with unit tests, and — in the spirit of the package — with a cross-check against an independent reference wherever one exists.