Casimir energy-momentum tensor for a brane in de Sitter spacetime

TL;DR

This paper calculates the vacuum energy-momentum tensor for a conformally coupled scalar field near a curved brane in de Sitter spacetime, revealing anisotropic stresses and boundary effects using conformal relations.

Contribution

It introduces a method to derive the vacuum energy-momentum tensor in de Sitter space from Rindler spacetime results, considering a curved brane with Robin boundary conditions.

Findings

Energy-momentum tensor is non-diagonal and anisotropic.

Vacuum stresses depend on boundary conditions and geometry.

Asymptotic behavior analyzed near horizon and boundary.

Abstract

Vacuum expectation values of the energy-momentum tensor for a conformally coupled scalar field is investigated in de Sitter (dS) spacetime in presence of a curved brane on which the field obeys the Robin boundary condition with coordinate dependent coefficients. To generate the corresponding vacuum densities we use the conformal relation between dS and Rindler spacetimes and the results previously obtained by one of the authors for the Rindler counterpart. The resulting energy-momentum tensor is non-diagonal and induces anisotropic vacuum stresses. The asymptotic behaviour of this tensor is investigated near the dS horizon and the boundary.