Parity violation in inflationary models

Parity symmetry is a fundamental property of the gravitational interaction in the description provided by General Relativity. Therefore its breaking could be a signal of deviation from such a standard model. Since inflation involves very high energy scales, it provides a unique window to test fundamental physics. In this thesis we study inflation within new parity violating theories of gravity that have been recently proposed. These theories generalize Chern-Simons gravity by including in the action coupling terms to gravity involving first and second derivatives of a scalar field (the inflaton field, in the context of inflation). Besides breaking parity, these theories also break Lorentz invariance. Our purposes are to see whether the new couplings lead to detectable parity breaking signatures in the power spectrum of primordial gravitational waves and whether they modify the tensor power spectrum, possibly leading to a blue power spectrum of primordial gravitational waves. Having a blue power spectrum means that the amplitude of tensor perturbations increases going to lower scales. This could be an important feature, because it could enhance the spectrum of primordial gravitational waves at scales relevant for interferometers. We find that the two circular polarization states evolve following different dynamical equations. Moreover, the speed of propagation of tensor modes is modified and aquires different values for the two polarization states during inflation. In the case of the theory with second derivatives of the scalar field we find that the term which corrects the tensor speed is however highly suppressed, working in the regime where we avoid the production of ghost fields. Hence the conclusions are analogous to the case with Chern-Simons gravity, both for the chirality in the tensor power spectrum and for the tensor spectral index. In the case of the theory with only first derivatives of the scalar field there is instead an additional contribution that modifies the tensor speed and which can be relevant if the couplings of the new operators have large time derivatives during inflation. We comment on possible interesting phenomenological signatures arising from this feature.