Cosmological Constraints on Cosmic Inflation and Scalar-Tensor Dark Energy Models from CMB Anisotropies and Galaxy Clustering

This thesis investigates the most recent cosmological bservations in order to constrain cosmic inflation and what is probably the simplest model of modified gravity. We provide a detailed calculation for the scalar spectral index and for the tensor-to-scalar ratio, in slow-roll approximation, for a selection of single field inflationary models and we compare them with Planck 2015 data, taking into account reheating uncertainties. We studied selected theoretically motivated parametrizations of the primordial power spectrum with departure from the near scale invariance, providing a better fit to the CMB temperature power spectrum with respect to the simplest slow-roll inflationary models. For a selection of models, we forecast the capability of future spectroscopic, photometric, and radio surveys, in combination with CMB measurements, to constrain parametrized features in the primordial power spectrum. We studied a simple class of modified gravity models alternative to ΛCDM, based on Induced Gravity, or a Brans-Dicke like, with a monomial potential with positive values of the exponent. Cosmological constraints for this class of dark energy models are derived from CMB alone and in combination with external dataset, such as BAO and H0 local measurements.