Relative information entropy in cosmology: The problem of information entanglement

• Main Author: Czinner, Viktor G.
• Publication Date: 2016
• Other Authors: Mena, Filipe C.
• Format: Article
• Language: eng
• Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
• Download full: https://hdl.handle.net/1822/41614
• topic: Cosmic inhomogeneities; Information entropy; Large scale structure; Ciências Naturais::Ciências Físicas; Ciências Naturais::Matemáticas; Science & Technology

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.