Tunneling and the Casimir effect on a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi></mml:math>-dimensional sphere

Two fundamental signatures of quantum field theory are tunneling and the Casimir effect. We examine the ground state energetic properties of a scalar field confined on a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>D</a:mi></a:math>-dimensional sphere and subjected to these two effects. We focus on <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>D</c:mi><c:mo>=</c:mo><c:mn>2</c:mn></c:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>D</e:mi><e:mo>=</e:mo><e:mn>3</e:mn></e:math>, with a negative coupling of a massless scalar field to curvature, providing a radius-dependent effective mass that triggers symmetry breaking. This scenario allows tunneling 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 <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>D</g:mi><g:mo>=</g:mo><g:mn>3</g:mn></g:math>, which could avoid a cosmological singularity. Published by the American Physical Society 2024