Covariant Perturbations Theory in General Multi-Fluids Cosmology

Abstract

We develop a variational approach, inspired by the work of Maldacena (Maldacena 2003, JHEP 0305), to study covariant cosmological perturbations in general multi-fluids extended gravity. A special attention is paid to the minimization of the propagating degrees of freedom to obtain simple equations of motion. In particular, by parametrizing perfect fluids with scalar fluids and by working within the ADM formalism, we manage to introduce new gauge invariant quantities, generalizing Mukhanov-Sasaki variables. Those developments are crucial to deeply understand the influence of general extended gravity either in the inflationary epoch or in the late-time inflation. In this proceeding, we present only the quadratic Lagrangian at first order for scalar perturbations deduced from the gravitational constraint equations.