New DBI Inflation model with Kinetic Coupling to Einstein Gravity

In this letter 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 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), which leads to a correction term of k 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.