Title:

Phenomenological tests of modified gravity

The main goal of this thesis is to test the viability of some modified theories of gravity suitable to describe gravitational phenomena at cosmological and astronomical scales. In the first part of the Thesis we study the viability of the BransDicke theory (BDT) and the effective scalartensor theory according (gBDT) to cosmological observations. We assume that either BDT as gBDT are limiting cases on very large scales of more general scalartensor theories involving derivative selfinteractions which have running Newton’s constant. In order to implement this assumption in a simple way we consider two types of models. The restricted models that correspond to the standard BDT with Newton constant today equal to measured Newton constant in solarsystem experiments. The unrestricted models, correspond to the case where the Newton’s constant today is a free parameter, and the cosmological GN is allowed to be different than in the solar system as in more general theories. We first explore the relevant theoretical aspects of these models. Afterwards, by using different analysis techniques we fitted cosmological observations. Finally we forecast limits of BDT by considering estimated covariance matrices for measurements of the matter power spectrum in redshift space from Euclid. The effective scalartensor theory gBDT arises from a phenomenological setup of parametrization of the LSS growth equations, we found estimates of modifications of the growth by using the correspondance between the estimates for the gBDT parameters. In the second part of the Thesis we present an extension of the Parameterized PostNewtonian (PPN) formalism that is able to handle Vainsteinian corrections. We argue that theories with a Vainshtein mechanism must be expanded using two small parameters. In this Parameterized PostNewtonianVainshteinian (PPNV) expansion, the primary expansion parameter which controls the PPN order is as usual the velocity v. The secondary expansion parameter, α, controls the strength of the Vainshteinian correction and is a theoryspecific combination of the Schwarzschild radius and the Vainshtein radius of the source that is independent of its mass. We present the general framework and apply it to the Cubic galileon theory both inside and outside the Vainshtein radius. The PPNV framework can be used to determine the compatibility of such theories with solar system and other strongfield data.
