An intrinsic cosmological observer

Abstract

There has been much recent interest in the necessity of an observer degree of freedom in the description of local algebras in semiclassical gravity. In this work, we describe an example where the observer can be constructed intrinsically from the quantum fields. This construction involves the slow-roll inflation example recently analyzed by Chen and Penington, in which the gauge-invariant gravitational algebra arises from marginalizing over modular flow in a de Sitter static patch. We relate this procedure to the Connes-Takesaki theory of the flow of weights for type III von Neumann algebras, and further show that the resulting gravitational algebra can naturally be presented as a crossed product. This leads to a decomposition of the gravitational algebra into quantum field and observer degrees of freedom, with different choices of observer being related to changes in a quantum reference frame for the algebra. We also connect this example to other constructions of type II algebras in semiclassical gravity, and argue they all share the feature of being the result of gauging modular flow. The arguments in this work involve various properties of automorphism groups of hyperfinite factors, and so in an appendix we review the structure of these groups, which may be of independent interest for further investigations into von Neumann algebras in quantum gravity.