Bound on largest $r\lesssim 0.1$ from sub-Planckian excursions of inflaton

Abstract

In this paper we will discuss the range of large tensor to scalar ratio, $r$, obtainable from a sub-Planckian excursion of a {\it single}, {\it slow roll} driven inflaton field. In order to obtain a large $r$ for such a scenario one has to depart from a monotonic evolution of the slow roll parameters in such a way that one still satisfies all the current constraints of \texttt{Planck}, such as the scalar amplitude, the tilt in the scalar power spectrum, running and running of the tilt close to the pivot scale. Since the slow roll parameters evolve non-monotonically, we will also consider the evolution of the power spectrum on the smallest scales, i.e. at ${\cal P}_{s}(k\sim 10^{16}~{\rm Mpc^{-1}})\lesssim 10^{-2}$, to make sure that the amplitude does not become too large. All these constraints tend to keep the tensor to scalar ratio, $r\lesssim 0.1$. We scan three different kinds of potential for supersymmetric flat directions and obtain the benchmark points which satisfy all the constraints. We also show that it is possible to go beyond $r\gtrsim 0.1$ provided we relax the upper bound on the power spectrum on the smallest scales.