Thermodynamics Positivity Bound from 3-Form Black Holes and Inflation with Higher-Derivative Corrections

TL;DR

This paper explores how thermodynamic bounds and higher-derivative corrections in 3-form gauge theories constrain black hole properties and inflation models, linking quantum gravity considerations with cosmological dynamics.

Contribution

It derives bounds on black hole masses and higher-derivative terms from thermodynamics and swampland criteria, and analyzes inflationary potentials within this framework.

Findings

Upper bound on extremal black hole mass in dS space

Higher-derivative corrections constrained by swampland criteria

Large-field inflation supported by Higgs-like potential

Abstract

We investigate the interplay between the thermodynamics 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 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 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.