New DBI Inflation model with Kinetic Coupling to Einstein Gravity

In this paper we study a new class of inflation models which generalize the Dirac-Born-Infeld (DBI) action with the addition of a nonminimal kinetic coupling (NKC) term. We dubbed this model as the {\it new DBI inflation model}. The NKC term does not bring new dynamical degree of freedom, so the equations of motion remain of second order. However, with such a coupling, the action is no longer linear with respect to the Einstein curvature term ($R$ or $G^{\mu\nu}$), which leads to a correction term of $k^4$ in the perturbations. The new DBI inflation model can be viewed as theories beyond Horndeski. Without violating nearly scale-invariance, such a correction may lead to new effects on the inflationary spectra that could be tested by future observations.