Theoretical and experimental constraints on modified gravity

In this thesis, we consider techniques to characterise a Solar System test for modified gravity theories with an inherent preferred acceleration scale (reducing to MOdified Newtonian Dynamics (MOND) in its non-relativistic limit). We further explore the use of measurements from the forthcoming LISA Pathfinder mission to test these theories. Employing gravitational wave techniques such as the expected signal-to-noise ratio as well as considering effects from a variety of instrumental noise models, saddle trajectories and systematics such as self gravity, we show such a test appears very viable. The possibility of constraints in the event of a null result is explored, as well as designing free functions to evade such a test. The symmetries present in such a scheme allowed us to we develop a simple algorithm for scaling tidal stresses in the event of parameters a_0 and k assuming values different to those originally considered (short cutting a lot of computational work). In doing so, we are able to show broadly, that the scaling of parameters (within an order of magnitude) could potentially save or slaughter a dubious result. Similarly constraints from fifth force experiments and bounds on anomalous accelerations on solar system scales could feed into our theories, but these would appear as parameters in the (otherwise unconstrained) free function μ. We present a similar scaling algorithm to rescale results previously computed from a particular μ, as well as look at methods to constrain it from data. We also explore the behaviour of previously poorly constrained parameters, such as the MONDian scaling C and its behaviour between models. We also extend our formalism to investigate results from more general free functions, perhaps resulting from scalar tensor or other modified gravity theories.