Tunnelling and the Casimir effect on a $D$-dimensional sphere

TL;DR

This paper investigates the combined effects of tunnelling and the Casimir effect on a massless scalar field confined to a D-dimensional sphere, revealing conditions where tunnelling dominates and discussing implications for early cosmology.

Contribution

It analyzes the interplay between tunnelling and Casimir effects on a scalar field in higher dimensions, highlighting regimes where tunnelling is more significant and exploring cosmological implications.

Findings

Tunnelling can dominate over the Casimir effect in certain parameter regimes.

The effective mass depends on the sphere's radius due to non-minimal coupling.

Potential to avoid cosmological singularities in D=3 scenarios.

Abstract

Two fundamental signatures of Quantum Mechanics are tunnelling and the Casimir effect. We examine the ground state energetic properties of a scalar field confined on a $D$-dimensional sphere, and subjected to these two effects. We focus on $D=2$ and $D=3$, with a non-minimal coupling of a massless scalar field to curvature, which provides a radius-dependent effective mass. This scenario allows tunnelling to be more important than the Casimir effect, in a certain regime of parameters, and potential implications in Early Cosmology are discussed for the case $D=3$, which could avoid a cosmological singularity.