A new inflation potential with NMC to gravity in light of Planck and BICEP2 data

In this paper we study a new inflation potential proposed in Belhaj et al. (Int J Mod Phys D 17:911–920, 2008 ), in the presence of a scalar field which interacts nonminimally with gravity. We present new constraints on the scalar spectral index n s , the tensor-to-scalar ratio r and running of the spectral index d n s d ln ( k ) from the recent data obtained by the Planck and BICEP2 experiment. The slow-roll parameters are reformulated in the case of a nonminimally coupled scalar field. We show that for parameter spaces of the models, inflation can occur at field values far below the four-dimensional Planck scale. We show also that for small and positive values of the nonminimal coupling ξ , the observational consequences of this model are in perfect compatibility with the latest observations data especially for N = 50 .