Probing gravity at the energy scale of inflation via primordial non-Gaussianity

In this thesis, we review the standard inflationary paradigm and study some inflationary models among the so-called α-attractors. Our main concern is the study of the inflationary dynamics and predictions, such as the primordial non-Gaussianity, of some α-attractor models. In order to study the bispectrum, we make use of the in-in formalism and the δN formalism. First, we focus on single-field models. We study the predictions of the α-attractors and the reasons underneath their universal behaviour. In particular, we analyse the acceptable initial conditions that lead to an inflationary era for the T-models. Secondly, we consider two-field α-attractor models in which one of the fields has a non-canonical kinetic term. We analyse their background dynamics and their predictions, especially for what concern mechanisms that can produce large non-Gaussianities thanks to the parameter α, the potential term and the non-canonical kinetic term. We consider two simple trajectories in field space: a circle and a nearly straight trajectory. In the former case, large non-Gaussianities can be produced thanks to the third derivative of the potential along the isocurvature direction or thanks to the non-canonical kinetic term. In the latter, they can be produced thanks to the α parameter or the non-canonical kinetic term. Finally, we study the background dynamics of two two-field models. In particular, we estimate the nonlinearity parameter fNL for the second one using the δN formalism.