Distance and de Sitter Conjectures on the Swampland

TL;DR

This work investigates whether a swampland constraint linking field-space distance to scalar potentials can be sharpened into a universal bound in controlled string-theory regimes. By combining the distance conjecture with Bousso's covariant entropy bound for accelerating universes, the authors derive a Refined de Sitter Conjecture: either $|\nabla V| \ge c M_p^{-1} V$ or the minimum Hessian eigenvalue satisfies $\min(\nabla_i\nabla_j V) \le - c' M_p^{-2} V$, with constants of order one; this bound remains valid where a traditional de Sitter vacuum would be ruled out. The paper provides evidence in weakly coupled regimes by analyzing tower-induced entropy growth and simple free-particle models, discusses cosmological implications, and situates the result within broader swampland program contexts, including connections to the Weak Gravity Conjecture and the Dine–Seiberg problem. It also clarifies why certain counterexamples to the original de Sitter conjecture do not evade the refined bound and outlines directions for testing the conjecture beyond parametric weak coupling.

Abstract

Among Swampland conditions, the distance conjecture characterizes the geometry of scalar fields and the de Sitter conjecture constrains allowed potentials on it. We point out a connection between the distance conjecture and a refined version of the de Sitter conjecture in any parametrically controlled regime of string theory by using Bousso's covariant entropy bound. The refined version turns out to evade all counter-examples at scalar potential maxima that have been raised. We comment on the relation of our result to the Dine-Seiberg problem.