  We compute the greybody factors for non-minimally coupled scalar fields in
four-dimensional Schwarzschild-de Sitter spacetime. In particular, we
demonstrate that the zero-angular-momentum greybody factor generically tends to
zero in the zero-frequency limit like frequency squared if there is
non-vanishing coupling to the scalar curvature. This is in contrast with the
minimally coupled case, where the greybody factor is known to tend to a finite
constant. We also study the Hawking radiation for non-minimally coupled
massless scalar fields in Schwarzschild-de Sitter spacetime, formulate a
sensible notion of a generalized absorption cross section and investigate its
properties.
