An accurate bound on tensor-to-scalar ratio and the scale of inflation

TL;DR

This paper derives a precise upper bound on the tensor-to-scalar ratio in single-field inflation models with sub-Planckian field excursions, linking inflationary parameters to particle physics constraints.

Contribution

It provides an analytical estimate of the maximum tensor-to-scalar ratio consistent with effective field theory and sub-Planckian field displacements during inflation.

Findings

Maximum tensor-to-scalar ratio r ≤ 0.12 for sub-Planckian inflation models.

Inflation models with field displacements below the Planck scale can still produce observable gravitational waves.

The bound connects inflationary physics with particle physics and effective field theory constraints.

Abstract

In this paper we provide an accurate bound on primordial gravitational waves, i.e. tensor-to-scalar ratio $(r)$ for a general class of single-field models of inflation where inflation occurs always below the Planck scale, and the field displacement during inflation remains sub-Planckian. If inflation has to make connection with the real particle physics framework then it must be explained within an effective field theory description where it can be trustable below the UV cut-off of the scale of gravity. We provide an analytical estimation and estimate the largest possible $r$, i.e. $r\leq 0.12$, for the field displacement less than the Planck cut-off.