  In this paper, we investigate the potential-driven inflation models with a
disformal coupling to Einstein Gravity, to find out the effects of such a
coupling on these models. We consider a simple coupling form which introduces
only one parameter, and three inflation models, namely the chaotic inflation,
the Higgs inflation, and the monodromy inflation. We find that the disformal
coupling can have some modifications to the observational variables of these
models such as the power spectrum, the spectral index as well as the
tensor/scalar ratio, although not too large due to the constraints on the
disformal coupling parameter. With these modifications, one has the opportunity
of improving models that lie on the edge of the favorable regions of Planck
observational data, such as monodromy inflation. Moreover, the non-trivial
sound speed of tensor perturbations (gravitational waves) may come out, due to
the coupling of gravity and kinetic terms of the field.
