A Class of Almost Equilibrium States in Robertson-Walker Spacetimes

TL;DR

This paper constructs a new class of states called 'almost equilibrium states' for quantum fields in non-stationary Robertson-Walker spacetimes, providing a way to describe thermal equilibrium without time symmetry.

Contribution

It introduces a novel method to define and minimize a free energy functional for quantum states in curved spacetime, resulting in physically meaningful thermal states.

Findings

Almost equilibrium states satisfy the Hadamard condition.

States of low energy are the ground states of these almost equilibrium states.

The construction provides the first example of thermal states in non-stationary spacetimes.

Abstract

In quantum field theory in curved spacetimes the construction of the algebra of observables of linear fields is today well understood. However, it remains a non-trivial task to construct physically meaningful states on the algebra. For instance, we are in the unsatisfactory situation that there exist no examples of states suited to describe local thermal equilibrium in a non-stationary spacetime. In this thesis, we construct a class of states for the Klein-Gordon field in Robertson-Walker spacetimes, which seem to provide the first example of thermal states in a spacetime without time translation symmetry. More precisely, in the setting of real, linear, scalar fields in Robertson-Walker spacetimes we define on the set of homogeneous, isotropic, quasi-free states a free energy functional that is based on the averaged energy density measured by an isotropic observer along his worldline. This functional is well defined and lower bounded by a suitable quantum energy inequality. Subsequently, we minimize this functional and obtain states that we interpret as 'almost equilibrium states'. It turns out that the states of low energy, which were recently introduced by Olbermann, are the ground states of the almost equilibrium states. Finally, we prove that the almost equilibrium states satisfy the Hadamard condition, which qualifies them as physically meaningful states.