In this report 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.
Recent data suggest that the Universe could be positively curved. Combined with an inflationary stage, this might lead to a curvature bounce instead of the Big Bang. The background evolution is presented, as a function of the parameters controlling the cosmic evolution. The primordial tensor spectrum is also calculated and possible observational footprints of the model are underlined. Several potentials are considered and general remarks are made about "naturalness" in this context.
We bring together two popular formalisms which generically parameterise deviations from General Relativity on astrophysical and cosmological scales, namely the parameterised post-Newtonian (PPN) formalism and the effective field theory (EFT) of dark energy and modified gravity. These separate formalisms are successfully applied to independently perform tests of gravity in their respective regimes of applicability on vastly different length scales. Nonlinear screening mechanisms indeed make it imperative to probe General Relativity across a wide range of scales. For a comprehensive interpretation of the complementary measurements it is important to connect them to effectively constrain the vast gravitational model space. We establish such a connection within the framework of Horndeski scalar-tensor theories restricted to a luminal propagation speed of gravitational waves. This is possible via the reconstruction of the family of linearly degenerate covariant Horndeski actions from the set of EFT functions and the subsequent derivation of the PPN parameters from the reconstructed theory. We outline the required conditions which ensure a reconstructed Horndeski model possesses a screening mechanism that enables significant modifications on cosmological scales while respecting stringent astrophysical bounds. Employing a scaling method, we then perform the general post-Newtonian expansion of the reconstructed models to derive their PPN parameters γ and β in their screened regimes.
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