Non-minimal derivative coupling gravity in cosmology
  We give a brief review of the non-minimal derivative coupling (NMDC) scalar
field theory in which there is non-minimal coupling between the scalar field
derivative term and the Einstein tensor. We assume that the expansion is of
power-law type or super-acceleration type for small redshift. The Lagrangian
includes the NMDC term, a free kinetic term, a cosmological constant term and a
barotropic matter term. For a value of the coupling constant that is compatible
with inflation, we use the combined WMAP9 (WMAP9+eCMB+BAO+ $H_0$) dataset, the
PLANCK+WP dataset, and the PLANCK $TT,TE,EE$+lowP+Lensing+ext datasets to find
the value of the cosmological constant in the model. Modeling the expansion
with power-law gives a negative cosmological constants while the phantom
power-law (super-acceleration) expansion gives positive cosmological constant
with large error bar. The value obtained is of the same order as in the
$\Lambda$CDM model, since at late times the NMDC effect is tiny due to small
curvature.
