Title: Generalised tests of gravity in cosmology

Abstract: A plethora of modified theories of gravity have been proposed over the last few decades. Testing them all observationally is a considerable challenge, so it is advantageous to develop theory-independent approaches that constrain deviations from General Relativity in a systematic way. Many of the most precise such constraints to date are obtained from astrophysical measurements, for which deviations from GR are described by the parameterised post-Newtonian (PPN) parameters. Some attempts have been made to perform similarly general tests on cosmological scales, but it is not clear that they refer to the same couplings as the PPN formalism does, and so interpreting results from these disparate regimes physically is difficult and potentially misleading. With that problem in mind, I will introduce a framework, called parameterised post-Newtonian cosmology, that allows information from cosmological and astrophysical regimes to be combined consistently. I will present novel constraints on the evolution of the PPN parameters over cosmic history, using data from CMB anisotropies and Solar System experiments concurrently, and I will explain how these ideas can be applied further to test cosmological gravity to high precision.