Sur la variation des constantes de Newton et d’Einstein

According to the general theory of relativity, the current paradigm for gravita- tion and concordant observational data, about 95% of the Universe’s content is only perceivable through gravitational effects. Consolidating the predictions of this theory is then of primordial importance. Those predictions are struc- tured around two dimensional constants : Newton’s and Einstein’s constants. The former, namely the universal constant, yields the universality of free fall of light and compact objects. The latter, also named cosmological constant, explains the late expansion acceleration of the Universe on cosmological scales. The main goal of this thesis is to explore the foundations of general relativity by promoting these constants as dynamical fields. First of all, we propose a generic test seeking for possible Newton’s constant variations in the primeval plasma. The modified weight of baryons translates the equilibrium point of the acoustic oscillations. A constraint on the amplitude of such variations is extracted from the anisotropies of the cosmic microwave background. Secondly, we scrutinize a simple modification of general relativity providing a minimal violation of the strong equivalence principle. Although the additional scalar field acts as a dark radiation at the cosmological expansion level, the imprint left on the matter field perturbations is clearly distinguishable from other radiations because of the particular scalar field anisotropic stress. Several constraints for this alternative gravitational theory are derived from the analy- sis of the cosmic microwave background, Type Ia supernovae and the measure of the Lemaˆıtre-Hubble constant. Finally, we replace the cosmological constant by a quintessence field. For selec- ted realistic models agreeing with current cosmological data, it is shown that the non-linear processes driving the growth of matter’s large scale structures encode the nature and the dynamics of dark energy. Although the confrontation between the investigated alternative ...