Quantum Breaking Bound on de Sitter and Swampland

TL;DR

This paper establishes a quantum breaking bound on de Sitter space, constraining scalar potentials and supporting the de Sitter swampland conjecture, with implications for string theory and inflation models.

Contribution

It derives a fundamental quantum consistency bound on de Sitter space that explains the de Sitter swampland conjecture and constrains inflationary scenarios.

Findings

Quantum breaking bounds restrict de Sitter longevity.

Constraints eliminate stable positive-energy minima.

Supports the de Sitter swampland conjecture.

Abstract

Quantum consistency suggests that any de Sitter patch that lasts a number of Hubble times that exceeds its Gibbons-Hawking entropy divided by the number of light particle species suffers an effect of quantum breaking. Inclusion of other interactions makes the quantum break-time shorter. The requirement that this must not happen puts severe constraints on scalar potentials, essentially suppressing the self-reproduction regimes. In particular, it eliminates both local and global minima with positive energy densities and imposes a general upper bound on the number of e-foldings in any given Hubble patch. Consequently, maxima and other tachyonic directions must be curved stronger than the corresponding Hubble parameter. We show that the key relations of the recently-proposed de Sitter swampland conjecture follow from the de Sitter quantum breaking bound. We give a general derivation and also illustrate this on a concrete example of $D$-brane inflation. We can say that string theory as a consistent theory of quantum gravity nullifies a positive vacuum energy in self-defense against quantum breaking.