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We define a distinguished "ground state" or "vacuum" for a free scalarquantum field in a globally hyperbolic region of an arbitrarily curvedspacetime. Our prescription is motivated by the recent construction of aquantum field theory on a background causal set using only knowledge of theretarded Green's function. We generalize that construction to continuumspacetimes and find that it yields a distinguished vacuum or ground state for anon-interacting, massive or massless scalar field. This state is defined forall compact regions and for many noncompact ones. In a static spacetime we findthat our vacuum coincides with the usual ground state. We determine it also fora radiation-filled, spatially homogeneous and isotropic cosmos, and show thatthe super-horizon correlations are approximately the same as those of a thermalstate. Finally, we illustrate the inherent non-locality of our prescriptionwith the example of a spacetime which sandwiches a region with curvaturein-between flat initial and final regions.

A Distinguished Vacuum State for a Quantum Field in a Curved Spacetime: Formalism, Features, and Cosmology