I will talk about a model in which a rolling pseudoscalar inflaton, through an axionic coupling to a U(1) gauge field, causes an amplification of the gauge field modes. After  briefly reviewing the rich phenomenology of the model, I will discuss the characterization of the spectrum of gravitational waves that are generated by the gauge field during inflation. On the more theoretical side, I will present an analytical study of the transition into the regime where the gauge quanta strongly backreact on the inflating background.