  We consider, in Palatini formalism, a modified gravity of which the scalar
field derivative couples to Einstein tensor. In this scenario, Ricci scalar,
Ricci tensor and Einstein tensor are functions of connection field. As a
result, the connection field gives rise to relation, $h_{\mu\nu} = f
g_{\mu\nu}$ between effective metric, $h_{\mu\nu}$ and the usual metric
$g_{\mu\nu}$ where $f \,=\,1 - \kappa{\phi}^{,\alpha}{\phi}_{,\alpha}/2 $. In
FLRW universe, NMDC coupling constant is limited in a range of $ -2/
\dot{\phi}^{2} < \kappa \leq \infty $ preserving Lorentz signature of the
effective metric. Slowly-rolling regime provides $\kappa < 0$ forbidding
graviton from travelling at superluminal speed. Effective gravitational
coupling and entropy of blackhole's apparent horizon are derived.
  In case of negative coupling, acceleration could happen even with $w_{\rm
eff} > -1/3$. Power-law potentials of chaotic inflation are considered. For $V
\propto \phi^2$ and $V \propto \phi^4$, it is possible to obtain
tensor-to-scalar ratio lower than that of GR so that it satisfies $r < 0.12$ as
constrained by Planck 2015 \cite{Ade:2015lrj}. The $V \propto \phi^2$ case
yields acceptable range of spectrum index and $r$ values. The quartic
potential's spectrum index is disfavored by the Planck results. Viable range of
$\k$ for $V \propto \phi^2$ case lies in positive region, resulting in less
blackhole's entropy, superluminal metric, more amount of inflation, avoidance
of super-Planckian field initial value and stronger gravitational constant.
