Relative information entropy in cosmology: The problem of information
  entanglement
  The necessary information to distinguish a local inhomogeneous mass density
field from its spatial average on a compact domain of the universe can be
measured by relative information entropy. The Kullback-Leibler (KL) formula
arises very naturally in this context, however, it provides a very complicated
way to compute the mutual information between spatially separated but causally
connected regions of the universe in a realistic, inhomogeneous model. To
circumvent this issue, by considering a parametric extension of the KL measure,
we develop a simple model to describe the mutual information which is entangled
via the gravitational field equations. We show that the Tsallis relative
entropy can be a good approximation in the case of small inhomogeneities, and
for measuring the independent relative information inside the domain, we
propose the R\'enyi relative entropy formula.
