The Lyth Bound of Inflation with a Tilt

TL;DR

This paper demonstrates that the inflationary field range can be universally inferred from measurements of spectral tilt and tensor-to-scalar ratio, significantly tightening the Lyth bound in the sub-Planckian regime.

Contribution

It establishes a model-independent method to determine the inflationary field range using observable parameters, strengthening the Lyth bound with current Planck data.

Findings

The field range can be inferred from $(n_s,r)$ measurements.

The Lyth bound is strengthened by two orders of magnitude.

For $n_s=0.96$, the bound on $r$ is reduced to $2 imes 10^{-5}$.

Abstract

We provide strong evidence for universality of the inflationary field range: given an accurate measurement of $(n_s,r)$, one can infer $\Delta \phi$ 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 $r \lesssim 2 \cdot 10^{-5}$.