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.

Bianchi I Model: An Alternative Way To Model The Presentday Universe

Although the new era of high precision cosmology of the cosmic microwave background (CMB) radiation improves our knowledge to understand the infant as well as the presentday Universe, it also leads us to question the main assumption of the exact isotropy of the CMB. There are two pieces of observational evidence that hint towards there being no exact isotropy. These are first the existence of small anisotropy deviations from isotropy of the CMB radiation and second, the presence of large angle anomalies, although the existence of these anomalies is currently a huge matter of debate. These hints are particularly important since isotropy is one of the two main postulates of the Copernican principle on which the FRW models are built. This almost isotropic CMB radiation implies that the universe is almost a FRW universe, as is proved by previous studies. Assuming the matter component forms the deviations from isotropy in the CMB density fluctuations when matter and radiation decouples, we here attempt to find possible constraints on the FRW type scale and Hubble parameter by using the Bianchi type I (BI) anisotropic model which is asymptotically equivalent to the standard FRW. To obtain constraints on such an anisotropic model, we derive average and late-time shear values that come from the anisotropy upper limits of the recent Planck data based on a model independent shear parameter of Maartens et al. (1995a,b) and from the theoretical consistency relation. These constraints lead us to obtain a BI model which becomes an almost-FRW model in time, and which is consistent with the latest observational data of the CMB.

Integrable Hierarchies and Information Measures

In this paper we investigate integrable models from the perspective of information theory, exhibiting various connections. We begin by showing that compressible hydrodynamics for a one-dimesional isentropic fluid, with an appropriately motivated information theoretic extension, is described by a general nonlinear Schrodinger (NLS) equation. Depending on the choice of the enthalpy function, one obtains the cubic NLS or other modified NLS equations that have applications in various fields. Next, by considering the integrable hierarchy associated with the NLS model, we propose higher order information measures which include the Fisher measure as their first member. The lowest members of the hiearchy are shown to be included in the expansion of a regularized Kullback-Leibler measure while, on the other hand, a suitable combination of the NLS hierarchy leads to a Wootters type measure related to a NLS equation with a relativistic dispersion relation. Finally, through our approach, we are led to construct an integrable semi-relativistic NLS equation.