Towards obtaining Green functions for a Casimir cavity in de Sitter spacetime

TL;DR

This paper develops a method to compute scalar Green functions for a Casimir cavity in de Sitter spacetime, enabling analysis of quantum field effects in curved backgrounds relevant to cosmology.

Contribution

It provides a first-order analytical solution for Green functions in de Sitter spacetime, facilitating the calculation of energy-momentum tensors in Casimir setups.

Findings

Derived explicit Green functions using special functions.

Enabled regularization and renormalization of energy-momentum tensor.

Applied results to scalar and electromagnetic fields.

Abstract

Recent work in the literature has studied rigid Casimir cavities in a weak gravitational field, or in de Sitter spacetime, or yet other spacetime models. The present review paper studies the difficult problem of direct evaluation of scalar Green functions for a Casimir-type apparatus in de Sitter spacetime. Working to first order in the small parameter of the problem, i.e. twice the gravity acceleration times the plates' separation divided by the speed of light in vacuum, suitable coordinates are considered for which the differential equations obeyed by the zeroth- and first-order Green functions can be solved in terms of special functions. This result can be used, in turn, to obtain, via the point-split method, the regularized and renormalized energy-momentum tensor both in the scalar case and in the physically more relevant electromagnetic case.