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.
