Non-minimal kinetic coupled gravity: inflation on the Warped DGP brane

We consider the non-minimally kinetic coupled version of DGP brane model, where the kinetic term of the scalar field is coupled to the metric and Einstein tensor on the brane by a coupling constant $\zeta$. We obtain the corresponding field equations, using the Friedmann-Robertson-Walker metric and the perfect fluid, and study the inflationary scenario to confront the numerical analysis of six typical scalar field potentials with the current observational results. We find that among the suggested potentials and coupling constants, subject to the e-folding $N=60$, the potentials $V(\phi)=\sigma\phi$, $V(\phi)=\sigma\phi^2$ and $V(\phi)=\sigma\phi^3$ provide the best fits with both Planck+WP+highL data and Planck+WP+highL+BICEP2 data.