The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes

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 104 to 105 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.