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In this paper we consider a massless scalar field, with a possible coupling$\xi$ to the Ricci scalar in a $D$ dimensional FLRW spacetime with a constantdeceleration parameter $q=\epsilon-1$, $\epsilon=-{\dot{H}}/{H^2}$. Correlationfunctions for the Bunch-Davies vacuum of such a theory have long been known tobe infrared divergent for a wide range of values of $\epsilon$. We resolvethese divergences by explicitly matching the spacetime under consideration to aspacetime without infrared divergencies. Such a procedure ensures that allcorrelation functions with respect to the vacuum in the spacetime of interestare infrared finite. In this newly defined vacuum we construct the coincidencelimit of the propagator and as an example calculate the expectation value ofthe stress energy tensor. We find that this approach gives both in theultraviolet and in the infrared satisfactory results. Moreover, we find that,unless the effective mass due to the coupling to the Ricci scalar $\xi R$ isnegative, quantum contributions to the energy density always dilute awayfaster, or just as fast, as the background energy density. Therefore, quantumbackreaction is insignificant at the one loop order, unless $\xi R$ isnegative. Finally we compare this approach with known results where theinfrared is regulated by placing the Universe in a finite box. In anaccelerating universe, the results are qualitatively the same, provided oneidentifies the size of the Universe with the physical Hubble radius at the timeof the matching. In a decelerating universe however, the two schemes givedifferent late time behavior for the quantum stress energy tensor. This happensbecause in this case the length scale at which one regulates the infraredbecomes sub-Hubble at late times.

Regulating the infrared by mode matching: A massless scalar in expanding spaces with constant deceleration