Cosmological perturbations in massive gravity and bigravity

This Thesis focus on two recent Lorentz-invariant theories which modify General Relativity by the introduction of an additional spin-2 field interacting with the space-time metric, the massive gravity theory and the bigravity (or bimetric gravity) theory. The main scopes of this Thesis are: first, to derive the full expression of the quadratic mass term for general perturbations at the level of the action both in the ghost-free massive gravity theory (with general reference metric) and in the ghost-free bimetric theory; and secondly, to investigate some cosmological applications of the linear perturbation theory to the case of bimetric gravity in order to see whether this theory can give rise to a viable description of our Universe, according to the current observational data. Part I of the Thesis is devoted to the first scope and part II to the second one