Gravitational Wave from Axion-SU(2) Gauge Fields: Effective Field Theory
  for Kinetically Driven Inflation
  Building on Weinberg's approach to effective field theory for inflation, we
construct an effective Lagrangian for a pseudo scalar (axion) inflaton field
with shift symmetry. In this Lagrangian we allow the axion field to couple to
non-Abelian gauge fields via a Chern-Simons term. We then analyze a class of
inflation models driven by kinetic terms. We find that the observational
constraints on the amplitudes of curvature perturbations and non-Gaussianity
yield a lower bound for the tensor-to-scalar ratio of $r\gtrsim 5\times
10^{-3}$ from the vacuum fluctuation. The sourced gravitational wave from SU(2)
gauge fields further increases the tensor-to-scalar ratio and makes the total
gravitational wave partially chiral and non-Gaussian, which can be probed by
polarization of the cosmic microwave background and direct detection
experiments. We discuss constraints on parameter space due to backreaction of
spin-2 particles produced by the gauge field.
