Casimir densities for a boundary in Robertson-Walker spacetime

TL;DR

This paper calculates the vacuum energy-momentum tensor for scalar and electromagnetic fields near a boundary in negatively curved Robertson-Walker spacetime, using conformal relations to Rindler spacetime results.

Contribution

It introduces a method to evaluate vacuum densities in curved spacetime with boundaries by relating them to Rindler spacetime results via conformal transformations.

Findings

Vacuum expectation values are expressed as boundary-free and boundary-induced parts.

Explicit formulas are derived for the energy-momentum tensor in Robertson-Walker spacetime.

The approach applies to general scale factors, broadening previous specific-case analyses.

Abstract

For scalar and electromagnetic fields we evaluate the vacuum expectation value of the energy-momentum tensor induced by a curved boundary in the Robertson--Walker spacetime with negative spatial curvature. In order to generate the vacuum densities we use the conformal relation between the Robertson-Walker and Rindler spacetimes and the corresponding results for a plate moving by uniform proper acceleration through the Fulling--Rindler vacuum. For the general case of the scale factor the vacuum energy-momentum tensor is presented as the sum of the boundary free and boundary induced parts.