de Sitter Decays to Infinity

TL;DR

This paper explores the conditions under which bubbles of nothing can form in models with stabilized extra dimensions and positive vacuum energy, analyzing decay processes in higher-dimensional theories.

Contribution

It maps bubble of nothing decay to a four-dimensional Coleman-De Luccia problem and provides criteria for their existence in stabilized de Sitter models.

Findings

Bubbles of nothing can exist without Coleman-De Luccia decay in some potentials.

When both decay processes are possible, bubble of nothing decay is usually faster.

The methods are applicable to various stabilizing potentials and internal geometries.

Abstract

Bubbles of nothing are a class of vacuum decay processes present in some theories with compactified extra dimensions. We investigate the existence and properties of bubbles of nothing in models where the scalar pseudomoduli controlling the size of the extra dimensions are stabilized at positive vacuum energy, which is a necessary feature of any realistic model. We map the construction of bubbles of nothing to a four-dimensional Coleman-De Luccia problem and establish necessary conditions on the asymptotic behavior of the scalar potential for the existence of suitable solutions. We perform detailed analyses in the context of five-dimensional theories with metastable $\text{dS}_4 \times S^1$ vacua, using analytic approximations and numerical methods to calculate the decay rate. We find that bubbles of nothing sometimes exist in potentials with no ordinary Coleman-De Luccia decay process, and that in the examples we study, when both processes exist, the bubble of nothing decay rate is typically faster. Our methods can be generalized to other stabilizing potentials and internal manifolds.