Tensor and scalar modes in axion inflation in the regime of strong homogeneous back-reaction.

The pseudo-scalar interaction between an axion inflaton and gauge fields can result in a strong amplification of the latter. The amplified gauge fields can (1) backreact on the background axion dynamics; (2) source an observable amount of gravitational waves (GW – tensor modes); (3) source significant axion inhomogeneities (scalar modes). The first two effects were studied together in the literature, under the assumption that the axion remains homogeneous (hence, the name homogeneous back-reaction). It was shown that, under this assumption, the sourced GW spectrum is characterized by peaks at different frequencies that might be detected at different GW observatories. This thesis includes the computation of the third effect, to determine whether and when the axion inhomogeneities become large, leading the system outside the regime of homogeneous back-reaction.