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arXiv · 2408.17189

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

Jean Alexandre·Drew Backhouse
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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.

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Jean Alexandre, Drew Backhouse. 2024-08-30. Tunnelling and the Casimir effect on a $D$-dimensional sphere. https://arxiv.org/abs/2408.17189

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