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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.

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.

We discuss the evolution and imprints of isocurvature initial conditions for the scalar field in scalar tensor extensions of Einstein gravity. We consider the simplest models of scalar tensor theories, as Induced gravity (IG, which can be recasted in form of Jordan-Brans-Dicke theory by a redefinition of the scalar field) or non-minimally coupled (NMC) scalar fields in which the acceleration of the Universe is connected to a variation of the effective Planck mass. After introducing the fundamental ideas of cosmological perturbation theory and scalar tensor theories of gravity, we give the evolution equations for matter, metric and scalar field fluctuations in synchronous gauge. We use this set of equations for both the IG and the NMC models to find a new isocurvature solution in which the scalar field fluctuations compensate for the relativistic components respectively. We also show how we can generalize the well known isocurvature modes in Einstein GR to these models. We show the different evolution of cosmological fluctuations for these isocurvature initial conditions compared to the standard adiabatic one. After that, we compute the CMB angular power spectrum for these solutions in the IG model, with the help of a modified Einstein-Boltzmann CLASS code. In particular the CMB power spectrum is computed separately for adiabatic and isocurvature initial conditions, i.e. for totally uncorrelated modes, and with arbitrary correlations leading to an interesting explanation of the lack of power in the low multipoles region of the CMB temperature power spectrum. Finally we show how a simple model of double inflation in IG could explain the generation of the new isocurvature mode.

We discuss the evolution and imprints of isocurvature initial conditions for the scalar field in scalar tensor extensions of Einstein gravity. We consider the simplest models of scalar tensor theories, as Induced gravity (IG, which can be recasted in form of Jordan-Brans-Dicke theory by a redefinition of the scalar field) or non-minimally coupled (NMC) scalar fields in which the acceleration of the Universe is connected to a variation of the effective Planck mass. After introducing the fundamental ideas of cosmological perturbation theory and scalar tensor theories of gravity, we give the evolution equations for matter, metric and scalar field fluctuations in synchronous gauge. We use this set of equations for both the IG and the NMC models to find a new isocurvature solution in which the scalar field fluctuations compensate for the relativistic components respectively. We also show how we can generalize the well known isocurvature modes in Einstein GR to these models. We show the different evolution of cosmological fluctuations for these isocurvature initial conditions compared to the standard adiabatic one. After that, we compute the CMB angular power spectrum for these solutions in the IG model, with the help of a modified Einstein-Boltzmann CLASS code. In particular the CMB power spectrum is computed separately for adiabatic and isocurvature initial conditions, i.e. for totally uncorrelated modes, and with arbitrary correlations leading to an interesting explanation of the lack of power in the low multipoles region of the CMB temperature power spectrum. Finally we show how a simple model of double inflation in IG could explain the generation of the new isocurvature mode.