De Sitter Space and the Swampland

TL;DR

This paper proposes a swampland criterion that constrains scalar potentials in quantum gravity, suggesting that stable de Sitter vacua are incompatible with consistent theories of quantum gravity.

Contribution

It introduces a new swampland criterion, $| abla V| ext{ } ext{geq} ext{ } c imes V$, which forbids de Sitter vacua and extends existing no-go theorems to more general accelerating universes.

Findings

Proposes a universal bound on scalar potentials in quantum gravity theories.

Shows that this bound rules out stable de Sitter vacua in string theory.

Extends no-go theorems to broader classes of accelerating universes.

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.