Natural Inflation on the brane with a TeV-scale gravity: Parameter constraints after Planck 2015

In the present work, we have studied Natural Inflation (NI) in the framework of the Randall-Sundrum II (RS-II) brane model in the light of the latest Planck results. Adopting the Randall-Sundrum fine-tuning, the model is characterized by three parameters in total, namely the five-dimensional (5D) Planck mass M5 and the two mass scales of the inflaton potential f and . We show in the ns-r plane the theoretical predictions of the model together with the allowed contour plots, and we conclude that the model is viable. By using the Planck results only, it is possible to determine the two mass scales of the inflaton potential in terms of M5, which remains undetermined. However, there are several good theoretical reasons to consider a higher-dimensional Planck mass of the order of 10TeV, which is compatible with primordial nucleosynthesis. If we insist on considering a M5 of this order of magnitude, all parameters are known and a sub-Planckian excursion of the inflaton scalar field is achieved.