Our understanding of the Universe is based on the ΛCDM model which, although the best cosmological model so far, relies on the presence of major unknown components – dark matter, dark energy, and an inflationary field – which in turn play a crucial role in the evolution of the Universe. These limitations of the model suggest that we may need to introduce modifications at cosmological scales. Indeed, a large variety of modified gravity theories have been proposed (see [1] for a review) and in order to better understand the behaviour of gravity in this regime, we must begin by constructing theoretical and observational tests of the ΛCDM model and the various alternative proposals.
This thesis is concerned with testing gravity on cosmological scales, by analysing the viability of alternative gravitational theories, and scrutinising their theoretical consistency. In order to do this, we take two approaches. On the one hand, we explore the viability of a specific modified gravity theory, namely massive bigravity. The evolution of a perfectly homogeneous and isotropic Universe has been previously studied in detail in this model, and has been found to fit observational data. Hence, in this thesis we analyse the evolution of linear cosmological perturbations, where we find a number of interesting instabilities. On the other hand, we take a broader view and develop a method for parametrising linear cosmological perturbations that stays agnostic about the underlying theory of gravity. We apply this method to three classes of models: scalar-tensor, vector-tensor and bimetric theories, and as a result, in this case, we identify the complete forms of the quadratic actions for linear perturbations, and the number of free parameters that need to be defined, to cosmologically characterise these broad classes of gravity theories.