Casimir effect for concentric spheres in de Sitter spacetime with signature change

TL;DR

This paper investigates the Casimir effect for concentric spheres in de Sitter spacetime with a signature change, revealing an additional constant pressure due to the Euclidean-Lorentzian transition.

Contribution

It introduces a novel geometric configuration with signature change and analyzes its impact on the Casimir effect in de Sitter space.

Findings

An extra constant pressure arises from the signature change.

The signature change influences the Casimir force behavior.

Discussion of implications for quantum field effects in curved spacetime.

Abstract

We revisit the Casimir effect for two concentric spherical shells in de Sitter background with a new geometric configuration, namely Euclidean signature between and Lorentzian signature outside the spheres with different cosmological constants, for a massless scalar field satisfying Dirichlet boundary conditions on the spheres. It is shown that an extra constant pressure emerges due to this signature changing configuration. Some interesting aspects of this extra term are then discussed.