The Lyth Bound of Inflation with a Tilt

Abstract

We provide strong evidence for universality of the inflationary field range: given an accurate measurement of $(n_s,r)$, one can infer $\hat{I}”\ddot{I}•$ in a model-independent way in the sub-Planckian regime for a range of universality classes of inflationary models. Both the tensor-to-scalar ratio as well as the spectral tilt are essential for the field range. Given the Planck constraints on $n_s$, the Lyth bound is strengthened by two orders of magnitude: whereas the original bound gives a sub-Planckian field range for $r\lesssim 2\cdot 10^{-3}$, we find that $n=0.96$ brings this down to $r\lesssim 2\cdot 10^{-5}$.

5 pages, 3 figures. v2: refs added, PRD version