Testing deviations from the ΛCDM model with electromagnetic and gravitational waves

The ΛCDM model has been extensively tested over the past decades and has been established as the standard model of cosmology. Despite its huge successes, it faces some serious theoretical problems, especially related to the nature of dark matter and dark energy. Different possible modifications and extensions have been considered in the past in order to solve these problems, and a question of central importance is how these modifications can be tested and experimentally distinguished from the standard case. The aim of this thesis is twofold. First, it presents two different modifications of the dark sector. A model in which dark matter forms a Bose-Einstein condensate in high density regions and in the process forms a non-minimal coupling to the metric is considered as a possible deviation from the cold dark matter scenario, while the possibility that dark energy is inhomogeneous in space is discussed as a possible deviation from a pure cosmological constant scenario. Second, it examines ways to test these possibilities via two main observational channels - gravitational waves and electromagnetic waves. The gravitational wave event GW170817 is used to test the dark matter model and to put constraints on the mass of the dark matter field and the strength of the nonminimal coupling. The luminosity distance and the redshift of light are highlighted as important observables for dark energy, and generalised theoretical formulae for these observables are derived for conformally FLRW and perturbed FLRW spacetimes. The luminosity distance and the redshift are finally used to test for possible anisotropies of the accelerated expansion of the universe.