Tunneling and the Casimir effect on a D-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 D-dimensional sphere and subjected to these two effects. We focus on D 1/4 2 and D 1/4 3, 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 D 1/4 3, which could avoid a cosmological singularity.