Evading the Lyth Bound in Hybrid Natural Inflation

TL;DR

The paper addresses the Lyth bound challenge for small-field inflation by proposing hybrid natural inflation, combining an axion-like shift symmetry with a waterfall end to inflation. Through a fluxbrane/Wilson line-inspired potential with a cosine modulation, it demonstrates that a sizable tensor-to-scalar ratio can arise during an initial slow-roll when $\epsilon$ is large, while the bulk of the required $60$ e-folds accumulate later when $\epsilon$ is small. Stringy constraints on the axion decay constant $f$ cap the maximal tensor signal to around $r\sim 10^{-3}$, and a curvaton mechanism is shown to be incompatible with these bounds. The scenario offers realistic prospects for detecting primordial tensors with future CMB and 21 cm experiments, while motivating further detailed string-theory modeling.

Abstract

Generically, the gravitational-wave or tensor-mode contribution to the primordial curvature spectrum of inflation is tiny if the field-range of the inflaton is much smaller than the Planck scale. We show that this pessimistic conclusion is naturally avoided in a rather broad class of small-field models. More specifically, we consider models where an axion-like shift symmetry keeps the inflaton potential flat (up to non-perturbative cosine-shaped modulations), but inflation nevertheless ends in a waterfall-regime, as is typical for hybrid inflation. In such hybrid natural inflation scenarios (examples are provided by Wilson line inflation and fluxbrane inflation), the slow-roll parameter $ε$ can be sizable during an early period (relevant for the CMB spectrum). Subsequently, $ε$ quickly becomes very small before the tachyonic instability eventually terminates the slow roll regime. In this scenario, one naturally generates a considerable tensor-mode contribution in the curvature spectrum, collecting nevertheless the required amount of e-foldings during the final period of inflation. While non-observation of tensors by Planck is certainly not a problem, a discovery in the medium to long term future is realistic.