Axion-gauge field dynamics with backreaction

Phenomenological success of inflation models with axion and SU(2) gauge fields relies crucially on control of backreaction from particle production. Most of the previous study only demanded the backreaction terms in equations of motion for axion and gauge fields be small on the basis of order-of-magnitude estimation. In this paper, we solve the equations of motion with backreaction for a wide range of parameters of the spectator axion-SU(2) model. First, we find a new slow-roll solution of the axion-SU(2) system in the absence of backreaction. Next, we obtain accurate conditions for stable slow-roll solutions in the presence of backreaction. Finally, we show that the amplitude of primordial gravitational waves sourced by the gauge fields can exceed that of quantum vacuum fluctuations in spacetime by a large factor, without backreaction spoiling slow-roll dynamics. Imposing additional constraints on the power spectra of scalar and tensor modes measured at CMB scales, we find that the sourced contribution can be more than ten times the vacuum one. Imposing further a constraint of scalar modes non-linearly sourced by tensor modes, the two contributions can still be comparable.