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

## TL;DR

This paper explores how adding a physical reference frame transforms the entanglement structure in quantum field theories, enabling finite entanglement fluctuations and connecting these ideas to cosmological predictions and high-temperature phases.

## Contribution

It introduces a method to convert type III factors into type II factors using a reference frame, linking quantum information concepts with cosmology and high-energy physics.

## Key findings

- Type II factors yield finite entanglement fluctuations.
- Mapping inflationary phase to type II factor predicts primordial power spectrum.
- Hagedorn phase fluctuations are described by large N matrix model eigenvalue distributions.

## 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.