Dynamical Critical Phenomena and Large Scale Structure of the Universe: the Power Spectrum for Density Fluctuations

TL;DR

This paper models the universe's structure formation using a generalized stochastic equation, revealing how noise and fluctuations lead to fractal galaxy distributions and matching observed power spectra.

Contribution

It introduces a novel application of a generalized stochastic equation to describe cosmic structure formation, linking dynamical critical phenomena to large-scale universe features.

Findings

Reveals fractal behavior in galaxy correlations at small scales.

Derives the Harrison-Zel'dovich spectrum from first principles.

Accounts for observed power spectrum features through renormalization group analysis.

Abstract

As is well known, structure formation in the Universe at times after decoupling can be described by hydrodynamic equations. These are shown here to be equivalent to a generalization of the stochastic Kardar--Parisi--Zhang equation with time-- dependent viscosity in epochs of dissipation. As a consequence of the Dynamical Critical Scaling induced by noise and fluctuations, these equations describe the fractal behavior (with a scale dependent fractal dimension) observed at the smaller scales for the galaxy--to--galaxy correlation function and $also$ the Harrison--Zel'dovich spectrum at decoupling. By a Renormalization Group calculation of the two--point correlation function between galaxies in the presence of (i) the expansion of the Universe and (ii) non--equilibrium, we can account, from first principles, for the main features of the observed shape of the power spectrum.