Natural Inflation on the brane with a TeV-scale gravity: Parameter   constraints after Planck 2015
  In the present work we have studied Natural Inflation in the framework of the Randall-Sundrum II brane model (RS-II) in the light of the latest Planck results. Adopting the Randall-Sundrum fine-tuning, the model is characterized by 3 parameters in total, namely the 5-dimensional Planck mass $M_5$ and the two mass scales of the inflaton potential $f$ and $\Lambda$. We show in the $n_s-r$ 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 $M_5$, which remains undetermined. However, there are several good theoretical reasons to consider a higher-dimensional Planck mass of the order of $10 TeV$, which is compatible with primordial nucleosynthesis. If we insist on considering a $M_5$ of this order of magnitude all parameters are known and a sub-Planckian excursion of the inflaton scalar field is achieved. 
Nelson Videla, Grigorios Panotopoulos
gr-qc