Primordial Non-Gaussianity and Primordial Tensor Modes

The discoveries in observational cosmology of the last two decades led to a tremendous progress in cosmology. From a theory with mainly qualitative ideas about the expanding universe originated from a state with high density and temper- ature (Hot Big Bang cosmological model), cosmology rapidly evolved to a quantita- tive science that culminated with the formulation of the so-called ΛCDM model in which the composition and the evolution of the universe are known well enough to make very detailed predictions for a large number of observables on many different scales. Nonetheless, the ΛCDM model lacks in giving a satisfactory explanation of the initial conditions that are necessary to explain the subsequent evolution of the uni- verse. The inflationary paradigm elegantly solves this problem, furthermore it pro- vides a solution for other issues that affect the standard cosmology such as the horizon and the flatness problems. Although the basic framework of inflationary cosmology is now well-established, the microphysical mechanism responsible for the accelerated expansion remains a mystery. In this thesis, we describe how the physics underlying inflation can be probed using the higher-order correlations of primordial density perturbations (non-Gaussianity). In particular, we focus on those correlation functions that involve primordial gravity waves (tensor modes). The importance of primordial tensor modes lies in their theoretical robustness: while scalar perturbations are sensitive to many details, tensor modes are much more model independent. In this thesis we start by stressing this robustness, focussing on tensor non-gaussianity. We show that in single-field models of inflation (i.e. within the framework of the Effective Field Theory of Inflation) the predictions for the correlation functions that involve tensor modes are pretty model independent: tensor bispectra can assume very few shapes. After having discussed the prediction of the simplest models we focus on the squeezed limit of the tensor-scalar-scalar 3-point function. The leading behaviour of this correlator is fixed by the so-called Tensor Consistency Relation in many inflationary theories. This model independent prediction is very robust and can be violated only in theories where there is an additional helicity-2 state besides the graviton or in models that enjoy a symmetry pattern different from the standard one. In the last part of this thesis we explore both these possibilities. First we intro- duce a set of rule that allow us to include light particles with spin in the Effective Field Theory of Inflation, then focussing on the phenomenology that arises from an additional light spin-2 field. Finally, we describe a model of inflation which is very peculiar and cannot be incorporated in the context of the Effective Field Theory of Inflation: Solid Inflation. Here the “stuff” that drives inflation has the same sym- metry as an ordinary solid. We show that even in solids some consistency relations among the non-gaussian correlators can still be derived