Perturbation Theory in k-Inflation Coupled to Matter
  We consider k-inflation models where the action is a non-linear function of
both the inflaton and the inflaton kinetic term. We focus on a scalar-tensor
extension of k-inflation coupled to matter for which we derive a modified
Mukhanov-Sasaki equation for the curvature perturbation. Significant
corrections to the power spectrum appear when the coupling function changes
abruptly along the inflationary trajectory. This gives rise to a modification
of Starobinsky's model of perturbation features. We analyse the way the power
spectrum is altered in the infrared when such features are present.
