Renormalization Group Approach in Newtonian Cosmology

TL;DR

This paper applies the renormalization group method to Newtonian cosmology, revealing fixed points and scaling behaviors of cosmological observables, and suggesting a possible fractal universe structure beyond the horizon.

Contribution

It introduces a novel RG approach to analyze scaling properties in Newtonian cosmology and identifies fixed points with implications for universe structure.

Findings

Identified three stable fixed points: Einstein-de Sitter, Milne, Quiescent.

Found that the density parameter decreases and the Hubble parameter increases at smaller scales.

Suggested the universe may have a fractal structure beyond the horizon.

Abstract

We apply the renormalization group (RG) method to examine the observable scaling properties in Newtonian cosmology. The original scaling properties of the equations of motion in our model are modified for averaged observables on constant time slices. In the RG flow diagram, we find three robust fixed points: Einstein-de Sitter, Milne and Quiescent fixed points. Their stability (or instability) property does not change under the effect of fluctuations. Inspired by the inflationary scenario in the early Universe, we set the Einstein-de Sitter fixed point with small fluctuations, as the boundary condition at the horizon scale. Solving the RG equations under this boundary condition toward the smaller scales, we find generic behavior of observables such that the density parameter $\Omega$ decreases, while the Hubble parameter $H$ increases for smaller averaging volume. The quantitative scaling properties are analyzed by calculating the characteristic exponents around each fixed point. Finally we argue the possible fractal structure of the Universe beyond the horizon scale.