``Natural'' Vacua in Hyperbolic Friedmann-Robertson-Walker Spacetimes

TL;DR

This paper constructs a natural vacuum state for a quantum scalar field in an open, hyperbolic Friedmann-Robertson-Walker universe, aligning late-time behavior with flat-spacetime quantum theory.

Contribution

It explicitly demonstrates how to define a vacuum, Fock space, and particle states in an open FRW universe, extending quantum field theory to hyperbolic cosmological models.

Findings

Defined a vacuum state consistent with flat spacetime at late times

Constructed Fock space and particle basis for the scalar field

Applicable to a radiation-dominated open universe

Abstract

Recent evidence indicates that the Universe is open, i.e., spatially hyperbolic, longstanding theoretical preferences to the contrary notwithstanding. This makes it possible to select a vacuum state, Fock space, and particle definition for a quantized field, by requiring concordance with ordinary flat-spacetime theory at late times. The particle-number basis states thus identified span the physical state space of the field at all times. This construction is demonstrated here explicitly for a massive, minimally coupled, linear scalar field in an open, radiation-dominated Friedmann-Robertson-Walker spacetime.