Scalar-tensor theories in light of cosmological tensions

In this PhD thesis, I study cosmologies within the simplest scalar-tensor theories of gravity consisting in a scalar field $\sigma$ non-minimally coupled to the Ricci scalar through a function $F(\sigma)$ that induces a time-variation in the Newton constant and a potential $V(\sigma)$. I explore the new physics in these cosmologies and use publicly available data to constrain them. Depending on the functional form of the non-minimal coupling and the potential, the cosmological dynamics changes significantly. For some of the models, the specific dynamics helps recover the consistency with very stringent tests of General Relativity from Solar System and laboratory experiments without the need of any screening mechanisms. When compared to publicly available data, all these models feature a value of the Hubble constant $H_0$ larger than the standard $\Lambda$CDM cosmology. This makes scalar-tensor theories one of the most interesting candidates to solve the $H_0$ tension which is becoming one of the most pressing questions in the post-Planck cosmology. In order to better characterize the phenomenology of scalar-tensor theories, I also investigate their degeneracy with parameters describing the physics of neutrinos. I show that bounds on the effective number of active neutrinos and their masses are slightly relaxed in this context, although they are only a very weakly degenerate with the modification to gravity studied in this thesis and the full inclusion of CMB and LSS data used here. Finally, I address the issue of initial conditions within these theories and present a new regular isocurvature mode connected with the variation of the Newton constant which is absent in Einstein gravity. Although the observational imprints are different, the allowed fraction of this mode, relative to the adiabatic one, is constrained by Cosmic Microwave Background data at a similar level to other known isocurvature modes.