Gauge invariant quantum backreaction in U(1) axion inflation

We evaluate the quantum backreaction due to a gauge field coupled to a pseudo-scalar field driving a slow-roll inflationary stage, the so-called axion inflation. The backreaction is evaluated for the first time using a gauge invariant approach, going to second order in perturbation theory, and taking into consideration inflaton fluctuations as well as scalar perturbations of the metric. Within our gauge-invariant, but observer-dependent approach, we naturally consider as physical observers the ones comoving with the inflaton field. Considering the effective expansion rate consequent to the gauge field's backreaction, we observe that the backreaction effect becomes significant quite rapidly, moving the system out of the perturbative regime and into what is often referred to as the strong backreaction regime. This behavior also applies to the parameter that dictates the production of the gauge fields. The space-time backreaction is mainly due to the helicity contribution within the region of validity of the perturbative regime. As a final result, we see that the evaluated backreaction goes in the direction of prolonging the inflationary period more compared to the scenarios previously studied.