The de Sitter Weak Gravity Conjecture from 3-Form Black Holes and Inflation with Higher-Derivative Corrections

Abstract: We investigate the interplay between the de Sitter (dS) Weak Gravity Conjecture (WGC) 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 extremal charged 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 obtain additional bounds on these terms, ensuring consistency with swampland criteria. We further analyze these corrections from a thermodynamic perspective, confirming that the Wald entropy remains compatible with the classical extremality bound. 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. 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 the dS WGC 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.