Boltzmann codes are used extensively by several groups for constraining cosmological parameters with Cosmic Microwave Background and Large Scale Structure data. This activity is computationally expensive, since a typical project requires from 10 4 to 10 5 Boltzmann code executions. The newly released code CLASS (Cosmic Linear Anisotropy Solving System) incorporates improved approximation schemes leading to a simultaneous gain in speed and precision. We describe here the three approximations used by CLASS for basic ΛCDM models, namely: a baryon-photon tight-coupling approximation which can be set to first order, second order or to a compromise between the two; an ultra-relativistic fluid approximation which had not been implemented in public distributions before; and finally a radiation streaming approximation taking reionisation into account.

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.

Short baseline neutrino oscillation experiments have shown hints of the existence of additional sterile neutrinos in the eV mass range. However, such neutrinos seem incompatible with cosmology because they have too large an impact on cosmic structure formation. Here we show that new interactions in the sterile neutrino sector can prevent their production in the early Universe and reconcile short baseline oscillation experiments with cosmology.