Chern-Simons gravity and fermions in axion-SU(2) gauge field models of inflation

In this thesis, we present two important consistency checks on axion-SU(2) gauge field model of in ation. Axion-SU(2) gauge field models of in ation consist of an SU(2) gauge field in an isotropic and homogeneous background, coupled to an axion field via a Chern-Simons term. This setup can source gravitational waves that come equipped with three distinctive features: they can be non-scale invariant, highly non-Gaussian, and circularly polarized. These features are unique and are not shared by canonical single scalar field in ation models. However, before such models can be taken seriously as feasible description of the early universe evolution, their theoretical consistency within established empirically possible settings, need to be asserted. With this goal in mind, we first examined the viability of in ation models with a spectator axion field coupled to both gravitational and SU(2) gauge fields via Chern-Simons couplings. Both parity-violating terms, i.e. gravitational Chern-Simons, and the other Chern-Simons term arise from the same underlying physics and exist simultaneously; hence they should be both treated on equal footing. Moreover, given that gravitational Chern-Simons terms may introduce ghost instabilities in the model, it is crucial to check the stability of the setup as well. As a result of this study, we found that the impact of these terms on the production and propagation of gravitational waves can be as large as a fifty percent enhancement. Moreover, using the phenomenological success of the axion-SU(2) sector, we can constrain the new free parameter, i.e. the coupling strength of the gravitational Chern-Simons term, in this setup. In the second study, we examined the particle production by a SU(2) gauge field coupled to a massive Dirac doublet. The reason for coupling these fields is that usually, couplings to other matter species can lead to particle production, which in turn induces backreaction on and destabilization of the stable, isotropic, and homogeneous configuration that the non-Abelian and axion backgrounds have during in ation. This coupling leads to a nontrivial mixing between fermion components of different avors and chirality, hence complicates the system of equations. To carry out the needed calculation we made two technical improvements compared to extant literature. First, we applied the antisymmetrization of the operators to treat particles and antiparticles on equal footing. Second, to deal with the UV divergences, we extended the idea of an existing instantaneous vacuum subtraction scheme. On the basis of both of these investigations, we conclude that the background dynamics of an axion-SU(2) sector remains unaffected and phenomenologically viable in the presence of the gravitational Chern-Simons term and massive fermions.