Consistency of Scalar Potentials from Quantum de Sitter Space

TL;DR

This paper explores the constraints on scalar potentials in quantum de Sitter space, linking tunneling rates, vacuum structure, and hierarchy problems, and extends the analysis of Coleman-De Luccia tunneling with gravity effects.

Contribution

It introduces new consistency conditions on scalar potentials in quantum de Sitter space and advances the understanding of Coleman-De Luccia tunneling beyond the thin-wall approximation.

Findings

Consistency conditions relate field space distance and vacuum energy scale.

Extended numerical analysis of tunneling for generic potentials.

Discussion on gravity's role in stabilizing the Standard Model potential.

Abstract

Consistency of the unconventional view of de Sitter space as a quantum theory of gravity with a finite number of degrees of freedom requires that Coleman-De Luccia tunneling rates to vacua with negative cosmological constant should be interpreted as recurrences to low-entropy states. This demand translates into two constraints, or consistency conditions, on the scalar potential which are generically: 1) the distance in field space between the de Sitter vacuum and any other vacuum with negative cosmological constant must be of the order of the reduced Planck mass or larger and 2) the fourth root of the vacuum energy density of the de Sitter vacuum must be smaller than the fourth root of the typical scale of the scalar potential. These consistency conditions shed a different light on both outstanding hierarchy problems of the Standard Model of particle physics: the scale of electroweak symmetry breaking and the scale of the cosmological constant. Beyond the unconventional interpretation of quantum de Sitter space, we complete the analytic understanding of the thin-wall approximation of Coleman-De Luccia tunneling, extend its numerical analysis to generic potentials and discuss the role of gravity in stabilizing the Standard Model potential.