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

Understand

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.