  We study a theory which generalizes the nonminimal coupling of matter to
gravity by including derivative couplings. This leads to several interesting
new dynamical phenomena in cosmology. In particular, the range of parameters in
which inflationary attractors exist is greatly expanded. We also numerically
integrate the field equations and draw the phase space of the model in second
order approximation. The model introduced here may display different
inflationary epochs, generating a non-scale-invariant fluctuation spectrum
without the need of two or more fields. Finally, we comment on the bubble
spectrum arising during a first-order phase transition occurring in our model.
