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

TL;DR

This paper introduces a new method to define a unique vacuum state for quantum fields in curved spacetimes, generalizing recent causal set approaches and analyzing its properties in various cosmological models.

Contribution

It provides a novel vacuum state construction based on retarded Green's functions applicable to arbitrary curved spacetimes, extending previous causal set methods to continuum theories.

Findings

The vacuum coincides with the usual ground state in static spacetimes.

In cosmological models, the state exhibits super-horizon correlations similar to thermal states.

The construction demonstrates inherent non-locality in curved spacetime quantum field theory.

Abstract

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. In a static spacetime we find that our vacuum coincides with the usual ground state. We determine it also for a radiation-filled, spatially homogeneous and isotropic cosmos, and show that the super-horizon correlations are approximately the same as those of a thermal state. Finally, we illustrate the inherent non-locality of our prescription with the example of a spacetime which sandwiches a region with curvature in-between flat initial and final regions.