Backreaction of axion-SU(2) dynamics during inflation

Abstract: We consider the effects of backreaction on axion-SU(2) dynamics during inflation. We use the linear evolution equations for the gauge field modes and compute their backreaction on the background quantities numerically using the Hartree approximation. We show that the spectator chromo-natural inflation attractor is unstable when back-reaction becomes important. Working within the constraints of the linear mode equations, we find a new dynamical attractor solution for the axion field and the vacuum expectation value of the gauge field, where the latter has an opposite sign with respect to the chromo-natural inflation solution. Our findings are of particular interest to the phenomenology of axion-SU(2) inflation, as they demonstrate the instability of the usual trajectory due to large backreaction effects. The viable parameter space of the model becomes significantly altered, provided future non-Abelian lattice simulations confirm the existence of the new dynamical attractor. In addition, the backreaction effects lead to characteristic oscillatory features in the primordial gravitational wave background that are potentially detectable with upcoming gravitational wave detectors.