Cosmology with non-minimal derivative couplings: perturbation analysis
  and observational constraints
  We perform a combined perturbation and observational investigation of the
scenario of non-minimal derivative coupling between a scalar field and
curvature. First we extract the necessary condition that ensures the absence of
instabilities, which is fulfilled more sufficiently for smaller coupling
values. Then using Type Ia Supernovae (SNIa), Baryon Acoustic Oscillations
(BAO), and Cosmic Microwave Background (CMB) observations, we show that,
contrary to its significant effects on inflation, the non-minimal derivative
coupling term has a negligible effect on the universe acceleration, since it is
driven solely by the usual scalar-field potential. Therefore, the scenario can
provide a unified picture of early and late time cosmology, with the
non-minimal derivative coupling term responsible for inflation, and the usual
potential responsible for late-time acceleration. Additionally, the fact that
the necessary coupling term does not need to be large, improves the model
behavior against instabilities.
