Probing parity violation in the Early Universe

In this thesis we briefly expose the shortcomings of the Hot Big-Bang model, thereby explaining the inflationary solution. Then, we describe a scalar single-field slow-roll model of Inflation, and introduce the topic of cosmological perturbation theory. After having summarized the standard ways to deal with cosmological perturbations, we introduce the gauge invariant scalar curvature perturbation field ζ, and explain why it is necessary to seek for its correlation functions of order higher than two in order to discriminate between inflationary models. We thus expose two important formalisms that allow us to treat cosmological correlation functions. The first one is the in-in formalism, which enables one to compute correlation functions in a similar way to what its done in the S-matrix approach. The second one is the ADM formalism, with which it turns out easier to take into account perturbations of the involved fields, in the context of General Relativity. We then apply these formalisms to two-, three-, and four-points correlation functions in the framework of single-field slow-roll Inflation, and of the I2(φ) ̃F F model, where the kinetic term of a gauge field is coupled to the inflaton. Finally, we introduce the f (φ) ̃W W model, which induces parity-violating signatures from the gravity sector. This model goes under the name of gravitional Chern-Simons term, coupling the inflaton with the Weyl tensor W . We then compute several two-, and three-points functions to highlight possible sources of parity violation. In the end, we compute the ⟨ζζζζ⟩ trispectrum mediated by tensor fields in the Chern-Simons model. This is indeed one of the main goals of this thesis: to see whether such a graviton-mediated trispectrum carries a parity-breaking signature. We investigate this possibility in details under several assumptions, discussing under which conditions ⟨ζζζζ⟩ turns out to be parity-violating.