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

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.