Scalar Tensor Gravity

According to the general theory of relativity, the current paradigm for gravitation 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 structured 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 analysis of the cosmic microwave background, Type Ia supernovae and the measure of the Lemaître-Hubble constant.

Finally, we replace the cosmological constant by a quintessence field. For selected 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 models and available cosmological data currently does not raise deviation to the concordant ΛCDM model, the present study shows that predictions and signatures of these models are unique compared to the standard scenario.

We construct an updated and extended compilation of growth rate data consisting of 34 points and including corrections for model dependence. In order to maximize the independence of the datapoints we also construct a subsample of this compilation (`Gold' growth dataset) which consists of 18 datapoints. We test the consistency of this dataset with the best fit Planck15/$\Lambda$CDM parameters in the context of General Relativity (GR) using the evolution equation for the growth factor $\delta(a)$ with a $w$CDM background. We find tension at the $\sim 3 \sigma$ level between the best fit parameters $w$ (the dark energy equation of state), $\Omega_{0m}$ (the matter density parameter) and $\sigma_8$ (the matter power spectrum normalization on scales $8h^{-1}$Mpc) and the corresponding Planck15/$\Lambda$CDM parameters. We show that the tension disappears if we allow for evolution of the effective Newton's constant, parametrized as $G_{eff}(a)/G_N = 1 + g_a(1-a)^n-g_a(1-a)^{2n}$ with $n\ge2$ where $g_a$, $n$ are parameters of the model, $a$ is the scale factor and $z = 1/a-1$ is the redshift. This parametrization satisfies three criteria: a. $G_{eff} > 0$, b. Consistency with Big Bang Nucleosynthesis ($G_{eff}(a\ll 1)/G_N=1$), c. Consistency with solar system tests ($G_{eff}(a=1)/G_N=1$ and $G_{eff}'(a=1)/G_N=0$). We show that the best fit form of $G_{eff}(z)$ obtained from the growth data corresponds to weakening gravity at recent redshifts (decreasing function of $z$) and we demonstrate that this behavior is not consistent with any scalar-tensor Lagrangian with a real scalar field. Finally, we use MGCAMB to find the best fit $G_{eff}(z)$ obtained from the Planck CMB power spectrum on large angular scales and show that it is a mildly increasing function of $z$, in $3\sigma$ tension with the corresponding decreasing best fit $G_{eff}(z)$ obtained from the growth data.

We study the evolution of homogeneous and isotropic, flat cosmological models within the general scalar-tensor theory of gravity with arbitrary coupling function and potential and scrutinize its limit to general relativity. Using the methods of dynamical systems for the decoupled equation of the Jordan frame scalar field we find the fixed points of flows in two cases: potential domination and

Scalar-tensor gravity theories with a nonminimal Gauss-Bonnet coupling typically lead to an anomalous propagation speed for gravitational waves, and have therefore been tightly constrained by multimessenger observations such as GW170817/GRB170817A. In this paper we show that this is not a general feature of scalar-tensor theories, but rather a consequence of assuming that spacetime torsion vanishes identically. At least for the case of a nonminimal Gauss-Bonnet coupling, removing the torsionless condition restores the canonical dispersion relation and therefore the correct propagation speed for gravitational waves. To achieve this result we develop a new approach, based on the first-order formulation of gravity, to deal with perturbations on these Riemann-Cartan geometries.