We consider slow-roll inflationary models in a class of modified theories of
gravity which contains non-minimal curvature-inflaton couplings, i.e., the
f(R,T) gravity, where R is the Ricci scalar and T is the trace of the
inflaton energy-momentum tensor. On top of the minimally coupled T that has
been widely investigated in the literature, we further include a RT mixing
term in the theory. This mixing term introduces non-minimal derivative
couplings and plays an important role in inflationary dynamics. Taking chaotic
and natural inflation as examples, we find that the predictions for spectral
tilt and the tensor-to-scalar ratio are sensitive to the existence of the RT
mixing term. In particular, by turning on this mixing term, it is possible to
bring chaotic and natural inflation into better agreement with observational
data.Comment: 16 pages, 4 figure