Casimir Forces for Robin Scalar Field on Cylindrical Shell in de Sitter Space

TL;DR

This paper derives formulas for Casimir forces on a cylindrical shell in de Sitter space for a massless scalar field with Robin boundary conditions, considering different cosmological constants inside and outside the shell.

Contribution

It provides the first detailed analysis of Casimir stresses for Robin boundary conditions on cylindrical shells in de Sitter space, including scenarios with varying cosmological constants.

Findings

Formulas for vacuum expectation values of energy-momentum tensor derived

Expressions for vacuum forces on cylindrical shells obtained

Analysis applicable to early universe domain wall formations

Abstract

The Casimir stress on a cylinderical shell in background of conformally flat space-time for massless scalar field is investigated. In the general case of Robin (mixed) boundary condition formulae are derived for the vacuum expectation values of the energy-momentum tensor and vacuum forces acting on boundaries. The special case of the dS bulk is considered then different cosmological constants are assumed for the space inside and outside of the shell to have general results applicable to the case of cylindrical domain wall formations in the early universe.