Entanglement, Observers and Cosmology: a view from von Neumann Algebras

TL;DR

The paper addresses the problem of divergent entanglement in local quantum field theory on horizons by embedding the horizon-observing region into a crossed-product framework with a physical reference frame, yielding a type $II$ von Neumann factor with finite entanglement fluctuations.The core method is to augment the local algebra ${ m A}( ext{D})$ with a clock-like reference-frame algebra satisfying $[t,h_{RF}]=-i$, producing a regularized modular Hamiltonian $h^{II}=h+eta h_{RF}$ and a dressed dynamics that supports density matrices and generalized entropy.The key contributions are (i) a detailed crossed-product construction connecting SS-charges, RFs, and localization, (ii) applications to de Sitter horizons and inflation where $ ext{Var}(h^{II})$ encodes the primordial power spectrum, and (iii) a large-$N$ gauge theory interpretation where Hagedorn physics is recast in a type $II$ setting with finite fluctuations and RF-induced entanglement capacity.This framework provides a potential predictive avenue for early-universe cosmology and holographic large-$N$ dynamics, by tying observable spectra and entanglement measures to the quantum structure of the observer's reference frame.

Abstract

Infinite entanglement fluctuations appear when a quantum field theory on a causally complete domain of space-time is a type $III$ factor. In the weak gravity limit $G_N=0$ this factor can be transformed into a crossed product type $II$ factor with finite entanglement fluctuations by adding a physical reference frame system (observer). The use of a physical reference frame to define a regularization of divergent entanglement is formally identical to the quantum information approach to superselection charges. In that case the added reference frame allows quantum superpositions between different superselection sectors. For the case of cosmological horizons we map the primordial inflationary slow rolling phase into a type $II$ modification of the pure de Sitter type $III$ factor and we use the so defined type $II$ finite entanglement fluctuations to predict the primordial power spectrum of scalar curvature fluctuations. For the Hagedorn high temperature phase of large $N$ Yang Mills, the type $II$ description of the Hagedorn phase accounts, in the large $N$ limit, for the quantum fluctuations of the interval of the corresponding matrix model eigenvalue distribution.