A Thermodynamic Positivity Bound on Higher-Derivative 3-Form Couplings in de Sitter, and its Inflationary Consequences

Abstract

We investigate the interplay between the thermodynamic positivity bounds and slow-roll inflation within a framework governed by a 3-form gauge field. Starting from classical considerations, we derive an upper bound on the mass of black holes in dS spacetime which constrains the admissible parameter space. To incorporate quantum gravity effects, we introduce higher-derivative corrections to the 3-form action and, by requiring the Wald entropy correction to be positive, obtain a strict bound on these terms. Evaluating the backreaction within a quasi-local thermodynamic cavity bounded by the zero-force surface, we find that the correction to the extremal mass vanishes, so that the exact Nariai state saturates the classical bound rather than being shifted below it. The resulting bound is found to be invariant under field redefinitions of the metric. Extending this setup to cosmological inflation, we examine the scalar dual of the 3-form in both large-field and small-field regimes. In the large-field limit, the potential acquires a Higgs-like structure that supports slow-roll inflation consistent with Planck data. In contrast, the small-field limit leads to an effective potential with an AdS minimum, rendering it inconsistent with the dS swampland constraints. Notably, we find that thermodynamic consistency can impose constraints more stringent than those derived from inflationary dynamics alone. These results underscore the utility of swampland-inspired principles in shaping viable models of early universe cosmology.