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 dS4× S1 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.
Highlights
Our Universe is entering a phase of dark energy domination
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
When u0 1 we find that the bubble of nothing (BON) and Coleman-De Luccia (CDL)/HM branches of solutions eventually merge together, with ∆S approaching the action of the CDL solution, ∆S ≈ ∆SCDL
Summary
Our Universe is entering a phase of dark energy domination. To date, cosmological observations are consistent with an epoch of late-time acceleration driven by a small and positive cosmological constant [1,2,3]. The scalar field plays the role of the radial modulus setting the size of the S1, and Witten’s solution is recovered in the case of a vanishing scalar potential This fourdimensional description, makes it natural to consider generalizations of the BON in the presence of a potential for the moduli, as first suggested in [32]. Our goals are to describe, from the four-dimensional perspective, existence criteria for BON solutions in theories with stabilized moduli; to develop analytic approximations for the BON action in the presence of a scalar potential; to compare the corresponding decay rate to those of the ordinary CDL and HM channels; and to study numerically those examples that are analytically intractable. A series of appendices collect various additional results of a more detailed or tangential nature and are referred to throughout the text
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