A Dynamical Approach to a Self-similar Universe

TL;DR

This paper introduces a non-relativistic dynamical model of a hierarchical universe that evolves into a self-similar structure, consistent with observed cosmic properties and providing insights into the universe's age.

Contribution

It presents a novel non-relativistic Lagrangian framework for modeling a hierarchical universe with self-similarity and derives implications for cosmic evolution and the Hubble law.

Findings

Universe evolves into a self-similar fractal structure

Model implies the Hubble law naturally

Estimated universe age consistent with observations

Abstract

We write a non-relativistic Lagrangian for a hierarchical universe. The equations of motion are solved numerically and the evolution of the fractal dimension is obtained for different initial conditions. We show that our model is homogeneous at the time of the last scattering, but evolves into a self-similar universe with a remarkably constant fractal dimension. We also show that the Hubble law is implied by this model and make an estimate for the age of the universe.