openIn axion-U(1) inflation models, in the limit of strong coupling between the inflaton and the gauge field, one helicity mode of the gauge field undergoes exponential enhancement. This amplification, governed by the inflaton velocity, leads to a delayed backreaction of the gauge field on the inflaton motion, resulting in oscillations in the inflaton velocity. In this thesis we conduct an analytical examination of the evolution equation, relaxing certain assumptions typically found in the literature. Additionally, we explore the numerical effects of a time-delayed friction term within a single-field inflation model.In axion-U(1) inflation models, in the limit of strong coupling between the inflaton and the gauge field, one helicity mode of the gauge field undergoes exponential enhancement. This amplification, governed by the inflaton velocity, leads to a delayed backreaction of the gauge field on the inflaton motion, resulting in oscillations in the inflaton velocity. In this thesis we conduct an analytical examination of the evolution equation, relaxing certain assumptions typically found in the literature. Additionally, we explore the numerical effects of a time-delayed friction term within a single-field inflation model
