The Cosmic Linear Anisotropy Solving System (CLASS) IV: Efficient implementation of non-cold relics

TL;DR

The paper addresses the computational challenge of incorporating massive, non-cold relics into Boltzmann codes by enabling arbitrary phase-space distributions and automatic momentum sampling. It introduces an adaptive quadrature strategy to optimize momentum-space sampling and a sub-Hubble fluid approximation that reduces the number of multipoles inside the Hubble radius, both implemented in CLASS. The dual approach yields substantial speedups (roughly a factor of 3 per massive neutrino) while preserving percent-level accuracy in CMB and matter-power spectra, and it proves flexible enough to handle non-thermal distortions and various warm dark matter production mechanisms. This work significantly enhances the practicality of precision cosmology with many non-cold relics, enabling efficient parameter estimation and model testing across diverse neutrino and dark matter scenarios.

Abstract

We present a new flexible, fast and accurate way to implement massive neutrinos, warm dark matter and any other non-cold dark matter relics in Boltzmann codes. For whatever analytical or numerical form of the phase-space distribution function, the optimal sampling in momentum space compatible with a given level of accuracy is automatically found by comparing quadrature methods. The perturbation integration is made even faster by switching to an approximate viscous fluid description inside the Hubble radius, which differs from previous approximations discussed in the literature. When adding one massive neutrino to the minimal cosmological model, CLASS becomes just 1.5 times slower, instead of about 5 times in other codes (for fixed accuracy requirements). We illustrate the flexibility of our approach by considering a few examples of standard or non-standard neutrinos, as well as warm dark matter models.