  The Feynman propagator in curved spacetime admits an asymptotic
(Schwinger-DeWitt) series expansion in derivatives of the metric. Remarkably,
all terms in the series containing the Ricci scalar R can be summed exactly. We
show that this (non-perturbative) property of the Schwinger-DeWitt series has a
natural and equivalent counterpart in the adiabatic (Parker-Fulling) series
expansion of the scalar modes in an homogeneous cosmological spacetime. The
equivalence between both R-summed adiabatic expansions can be further extended
when a background scalar field is also present.
