Stability in Axion Inflation with Strong Backreaction from a Massive Vector Boson

We study a modification of the model of axion inflation coupled to a $U(1)$ gauge field where the vector field is massive. In the conventional scenario with a massless gauge field, the onset of the regime where the gauge field strongly backreacts on the inflaton displays an instability whose nonlinear evolution and endpoint remain poorly understood. We argue that, if the gauge field is massive enough, the transition to the strong backreaction regime instead occurs smoothly, avoiding this instability. This observation suggests that axion inflation with massive gauge fields admits a controllable strong backreaction regime, so that a phenomenologically viable realization of inflation might be possible in this class of models.