De Sitter Space and the Swampland

TL;DR

The authors introduce the swampland bound $|∇V| \ge c \cdot V$ as a universal constraint against metastable de Sitter vacua in quantum gravity, motivating it through string-theory no-go theorems and energy conditions. They quantify the bound in explicit constructions across M-theory and various string theories, showing order-one lower limits on the potential slope and saturations in known AdS compactifications, while noting the bound’s compatibility with quintessence. They further relate these bounds to SEC/NEC, discuss their non-universality in the presence of energy-condition violations, and extend the analysis to constraints on accelerating universes and laboratory setups, including a Farhi–Guth-style censorship of small-slope, positive-V regions. Overall, the results strengthen the case that de Sitter vacua are generically incompatible with controlled string constructions and bolster quintessence-like cosmologies as viable alternatives.

Abstract

It has been notoriously difficult to construct a meta-stable de Sitter (dS) vacuum in string theory in a controlled approximation. This suggests the possibility that meta-stable dS belongs to the swampland. In this paper, we propose a swampland criterion in the form of $|\nabla V|\geq\ c \cdot V$ for a scalar potential $V$ of any consistent theory of quantum gravity, for a positive constant $c$. In particular, this bound forbids dS vacua. The existence of this bound is motivated by the abundance of string theory constructions and no-go theorems which exhibit this behavior. We also extend some of the well-known no-go theorems for the existence of dS vacua in string theory to more general accelerating universes and reinterpret the results in terms of restrictions on allowed scalar potentials.