Covariant approach to parametrized cosmological perturbations

We present a covariant formulation for constructing general quadratic actions for cosmological perturbations, invariant under a given set of gauge symmetries for a given field content. This approach allows us to analyze scalar, vector, and tensor perturbations at the same time in a straightforward manner. We apply the procedure to diffeomorphism invariant single-tensor, scalar-tensor, and vector-tensor theories and show explicitly the full covariant form of the quadratic actions in such cases, in addition to the actions determining the evolution of vector and tensor perturbations. We also discuss the role of the symmetry of the background in identifying the set of cosmologically relevant free parameters describing these classes of theories, including calculating the relevant free parameters for an axisymmetric Bianchi-I vacuum universe.