Perturbation technique for quantum fields in curved space

We derive a concrete expression for the vacuum expectation value of the stress tensor for a massless, nonconformal scalar field propagating in a background spatially flat Robertson-Walker spacetime, up to second order in perturbation theory in the conformal-breaking parameter. The result, which is valid for an arbitrary Robertson-Walker scale factor (subject only to vanishing scalar curvature at some moment) is manifestly nonlocal, yet can still be written as an integral expression in closed form. The method should be extendible to the massive field and anisotropic spacetime cases.