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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. Weshow that this (non-perturbative) property of the Schwinger-DeWitt series has anatural and equivalent counterpart in the adiabatic (Parker-Fulling) seriesexpansion of the scalar modes in an homogeneous cosmological spacetime. Theequivalence between both R-summed adiabatic expansions can be further extendedwhen a background scalar field is also present.

R-summed form of adiabatic expansions in curved spacetime