The currently accepted standard model of cosmology uses general relativity with a ΛCDM matter content to describe the universe on the largest scales. It is an overwhelmingly successful theory, consistent with all observational tests. Despite this, theoretically unsatisfying elements to the theory exist and these have motivated various theories of modified gravity that challenge general relativity. In order to pass the stringent observational tests on a solar system level, the deviation of modified gravities from general relativity must be suppressed. This is known as screening, and different modified gravity theories use different screen- ing mechanisms. We motivate modifying gravity and the need for screening mechanisms. Three explicit models of modified gravity which exhibit screening are presented. These are the Galileon, K-mouflage and Chameleon models. In this thesis we investigate several aspects of these models.

We study astrophysical black holes in Galileon and K-mouflage theories. The no-hair theorem of General Relativity states that, under certain specific assumptions, the scalar field is trivial around a black hole. The assumptions going into the no-hair theorem are the absence of external matter and time independence. An astrophysical black hole typically has an accretion disk, so automatically circumvents the no-hair theorem. We display the scalar field profile around such black holes, compute the fifth force and demonstrate that the work done by the fifth force is small compared to the energy lost due to radiation in General Relativity. Further we drop the assumption of a static black hole and investigate the time- dependent solution of the scalar field in both theories. We find exact time-dependent vacuum K-mouflage black hole solutions and further consider time-dependent solutions with an ac- cretion disk. For K-mouflage the solution is similar to the time-independent one whereas the Galileon theories solutions resembles closely the time-dependent vacuum solution.

The most general coupling of the scalar field to matter contains both a conformal and disformal term. We investigate the effect of a disformal coupling in K-mouflage theories, calculating the cosmological background evolution of the theory and extending our results on the behaviour of the scalar field around a black hole to include the disformal coupling. We find that large regions of the parameter space provide only percent level deviations from the ΛCDM evolution, despite qualitative differences from the conformal-only case.

Often spherical symmetry is assumed to demonstrate the screening of K-mouflage theories. We present preliminary calculations exploring the effect the shape of a source object has on the scalar field it generates. We find that the shape dependence is similar to that of the D-BIon, another theory that screens when the first derivative of the field is large. In particular we find that screening is strongest for planar objects, in contrast to Galileon theories for which screening is entirely absent.

We move on from K-mouflage theories to consider Chameleon theories. We propose a logarithmic potential, which differs from the standard power law potential usually assumed, and use observational data to constraint the parameter space of the theory.