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 .