Evading the Lyth bound in hybrid natural inflation

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 axionlike shift symmetry keeps the inflaton potential flat (up to nonperturbative 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 cosmic microwave background 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 nonobservation of tensors by Planck is certainly not a problem, a discovery in the medium- to long-term future is realistic.