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A covariant vacuum state for free quantum field theory in curved spacetimes

A well known unsatisfactory feature of quantum field theory on curved spacetimes is the lack of a unique notion of vacuum. This ambiguity is typically attributed to the fact that the usual formulation of quantum field theory makes crucial use of properties which are only specific to Minkowski space (e.g. Poincare invariance, Fourier transform etc). Moreover, if spacetime is to be described by a discrete structure (such as a causal set), the whole quantization machinery available in the continuum (e.g. the Klein-Gordon solution space) becomes highly nontrivial. In this talk, I will propose a distinguished vacuum state for a free quantum field in a globally hyperbolic region of  an arbitrarily curved spacetime . This 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. I will argue that this construction can be naturally generalized  to continuum spacetimes and that it yields a distinguished vacuum or ``ground state'' for a non-interacting, massive or massles scalar field. Lastly, I will present concrete predictions of this proposal as applied to static spacetimes, de Sitter space,  and a radiation-dominated cosmos.