Dark energy in Lorentz violating and non-local modified gravity theories

Evidence suggests that our Universe is currently undergoing a period of accelerated expansion and the phenomenon behind this is typically referred to as dark energy. The origin behind this is still not yet fully understood and, as such, a large number of different explanations have been posited in an attempt to describe the nature of dark energy. This has led to a very large number of different possible modified gravity theories and dark energy models which need to be dealt with in a systematic manner. Parametrized approaches attempt to deal with these different theories by compressing the large freedom afforded to us into a relatively small number of phenomenological functions, which are able to describe many different types of theories. In this thesis, we predominantly work with the Equation of state approach for the perturbations, which treats a modified gravity theory or dark energy model as a new cosmological fluid. It then parametrizes the dynamics of the perturbations in this fluid via the gauge invariant anisotropic stress and entropy perturbation. In particular, we investigate the evolution of cosmological perturbations in Lorentz violating models described by a time-like unit normalized vector field with non-canonical kinetic terms, in what are called generalized Einstein-Aether models. We develop a designer approach for these models so that their background is fixed to LCDM or wCDM, allowing us to focus on the impact of the perturbations. We then explore whether their cosmological signatures are compatible with the Cosmic Microwave Background temperature anisotropy, polarization, and lensing data. We find that, along with recent constraints from gravitational waves, many of these models are forced to be very similar to LCDM, but there is still some leeway for these models to be compatible with the data. We then investigate the constraints imposed by the recent observation of coincident gravitational waves and gamma rays more generally, in the context of so-called non-local theories of gravity. We develop a possible suppression mechanism which would allow modified gravity theories to evade the stringent constraints and find that, in non-local models, a linear screening mechanism for the scalar perturbations naturally arises to suppress the effects of modified gravity.