Ricci curvature non-minimal derivative coupling cosmology with field re-scaling

In this letter, cosmology of a simple NMDC gravity with $\xi R \phi_{,\mu}\phi^{,\mu}$ term and a free kinetic term is considered in flat geometry and in presence of dust matter. A logarithm field transformation $\phi' = \mu \ln \phi$ is proposed phenomenologically. Assuming slow-roll approximation, equation of motion, scalar field solution and potential are derived as function of kinematic variables. The field solution and potential are found straightforwardly for power-law, de-Sitter and super-acceleration expansions. Slow-roll parameters and slow-roll condition are found to depend on more than one variable. At large field the re-scaling effect can enhance the acceleration. For slow-rolling field, the negative coupling $\xi$ could enhance the effect of acceleration.