Connection between Fisher Information and Wave Mechanical
  Interpretations of Universe
  In this study, we model the dark matter and baryon matter distribution in the
Cosmic Web by means of highly nonlinear Schr\"{o}dinger type and reaction
diffusion wave mechanical descriptions. The construction of these wave
mechanical models of the structure formation is achieved by introducing the
Fisher information measure and its comparison with a highly nonlinear term
called the quantum potential in the wave equations. Strikingly, the comparison
of the nonlinear term and the Fisher information measure provides a dynamical
distinction between lack of self-organization and self-organization in the
dynamical evolution of the cosmic components. Mathematically equivalent to the
standard cosmic fluid equations, these approaches make it possible to follow
the evolution of the matter distribution even into the highly nonlinear regime
by circumventing singularities. In addition, these wave formalisms are extended
to two-fluid descriptions of the coupled dark matter and baryon matter
distributions in the linear regime, in the Einstein de Sitter Universe (EdS) to
construct toy models of the cosmic components in this relatively simple
Universe model. Based on these two different wave mechanical formalisms, here
fully analytical results for the dark matter and baryon distributions are
provided. Also, numerical realizations of the emerging weblike patterns are
presented from the nonlinear dynamics of the baryon component corresponding to
soliton-like solutions. These soliton-like solutions might represent a proper
description of filamentary structures even in the linear regime.
