Review on tests of General Relativity And Modified Gravity Using Pulsar Timing

In this review we aim to describe the most stringent tests of the strong equivalence principle, the fundamental principle of General Relativity, using pulsar timing. For this purpose, we first construct the parametrized post-Newtonian and post-Keplerian formalism together with their parameters. Then we constrain the post-Newtonian parameters associated to the violation of the strong equivalence principle with the most stringent tests using pulsar timing techniques. We will in particular see that these bounds are the most constraining limits on a violation of the principle. Finally we will discuss the implication of these results on scalar-tensor theories as well as massive gravity. We will find that the set of possible scalar-tensor theories can be tightly reduce, however in the case of massive gravity, the level of precision is not sufficient to probe the predicted mass of the graviton.