Casimir Effect for Spherical Shell in de Sitter Space

TL;DR

This paper calculates the Casimir stress on a spherical shell in de Sitter space for a massless scalar field, analyzing how vacuum energy differences influence bubble dynamics in a cosmological context.

Contribution

It provides a detailed calculation of Casimir stress in de Sitter space considering different vacuum backgrounds and explores the resulting bubble evolution.

Findings

Bubbles with small vacuum energy differences expand.

Bubbles with large vacuum energy differences collapse.

No particle creation occurs despite time-dependent metric.

Abstract

The Casimir stress on a spherical shell in de Sitter background for massless scalar field satisfying Dirichlet boundary conditions on the shell is calculated. The metric is written in conformally flat form. Although the metric is time dependent no particles are created. The Casimir stress is calculated for inside and outside of the shell with different backgrounds corresponding to different cosmological constants. The detail dynamics of the bubble depends on different parameter of the model. Specifically, bubbles with true vacuum inside expand if the difference in the vacuum energies is small, otherwise they collapse.