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

Understand

We define a distinguished "ground state" or "vacuum" for a free scalar quantum field in a globally hyperbolic region of an arbitrarily curved spacetime.

• Our prescription is motivated by the recent construction of a quantum field theory on a background causal set using only knowledge of the retarded Green's function.
• We generalize that construction to continuum spacetimes and find that it yields a distinguished vacuum or ground state for a non-interacting, massive or massless scalar field.
• This state is defined for all compact regions and for many noncompact ones.