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.Comment: 13 pages, special issue review article. In the final version, the
calculations of Sec. III have been improved, two References have been added
and their content has been summarize