Tensions and challenges for cosmological perturbations theory

A few tensions in observational data are challenging the standard cosmological model, the most prominent one being the Hubble tension. Several extensions of the minimal LambdaCDM model - featuring a more complicated background, thermal and perturbation history - have been proposed as potential solutions. I will summarise our recent efforts to classify such models and compare their tension-solving performances. This work relies mainly on the development of the cosmology simulation code CLASS. I will also review the various directions in which CLASS is currently being extended, in particular, for predicting the properties of anisotropies in the gravitational wave background.