Classical, quantum and numerical aspects of modified theories of gravity

This thesis considers modifications of some specific and well-known gravity theories. In particular, linearised infinite-derivative gravity theories are studied in both four-dimensional and two-dimensional space-time. For the four-dimensional case, some specific quantum aspects of infinite-derivative gravity are examined. This includes an examination of the non-static potential that arises in such a theory when two spinless particles exchange a graviton. Infinite-derivative modifications of two specific two-dimensional gravity theories that have a dilaton field are also constructed in the linearised regime. Non-local modifications to the linearised black-hole solutions of the local theories are then obtained. It is found that the obtained linearised non-local solutions are free of the singular nature that is present in the local case. Finally, a numerical relativity code is constructed to study the evolution of a massless scalar field in the context of the four-dimensional Starobinsky gravity model which is a modification of Einstein’s theory of General Relativity.