Covariant and quasi-covariant quantum dynamics in Robertson-Walker space-times

TL;DR

This paper develops a framework for describing quantum dynamics in Robertson-Walker space-times, introducing covariant and quasi-covariant dynamics, and demonstrates their existence via transplantation from de Sitter space.

Contribution

It introduces a canonical method to define quantum dynamics in Robertson-Walker space-times, including covariant and quasi-covariant cases, using a novel transplantation technique from de Sitter space.

Findings

Existence of quasi-covariant quantum dynamics in Robertson-Walker space-times.

A method to transplant states and local algebras from de Sitter to Robertson-Walker space.

Transplanted states are locally passive with respect to the constructed dynamics.

Abstract

We propose a canonical description of the dynamics of quantum systems on a class of Robertson-Walker space-times. We show that the worldline of an observer in such space-times determines a unique orbit in the local conformal group SO(4,1) of the space-time and that this orbit determines a unique transport on the space-time. For a quantum system on the space-time modeled by a net of local algebras, the associated dynamics is expressed via a suitable family of ``propagators''. In the best of situations, this dynamics is covariant, but more typically the dynamics will be ``quasi-covariant'' in a sense we make precise. We then show by using our technique of ``transplanting'' states and nets of local algebras from de Sitter space to Robertson-Walker space that there exist quantum systems on Robertson-Walker spaces with quasi-covariant dynamics. The transplanted state is locally passive, in an appropriate sense, with respect to this dynamics.