  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.
