States of Low Energy in Homogeneous and Inhomogeneous, Expanding Spacetimes

TL;DR

This paper constructs and analyzes low-energy states for the Klein-Gordon field in both homogeneous and inhomogeneous expanding spacetimes, ensuring they are Hadamard and generalize previous models.

Contribution

It introduces a method to construct states that minimize energy density in complex spacetimes, extending prior work to more general settings.

Findings

States minimize energy density for Klein-Gordon field

States are proven to be Hadamard

Generalizes previous low-energy state constructions

Abstract

We construct states on the algebra of the Klein-Gordon field that minimize the energy density in homogeneous and in inhomogeneous spacetimes, both with compact Cauchy hypersurfaces. The energy density is measured by geodesic observers and smeared over a spacelike slab of spacetime, entirely containing a Cauchy hypersurface and extended in time. We further show that these states are Hadamard states. The present construction generalizes the construction of States of Low Energy in Robertson-Walker spacetimes presented by Olbermann (2007).