Exact isotropic cosmologies with local fractal number counts

TL;DR

This paper develops an exact relativistic cosmological model featuring a local inhomogeneous fractal distribution that smoothly transitions to a homogeneous universe at large scales, revealing implications for the Hubble law and cosmic density.

Contribution

It introduces a novel exact cosmological solution with local fractal inhomogeneity matching to a homogeneous background, advancing understanding of cosmic structure and expansion.

Findings

Inhomogeneous local region exhibits fractal number counts.

Matching conditions imply a nonlinear Hubble law or low large-scale density.

Model bridges local fractal structures with global homogeneity.

Abstract

We construct an exact relativistic cosmology in which an inhomogeneous but isotropic local region has fractal number counts and matches to a homogeneous background at a scale of the order of $10^2$ Mpc. We show that Einstein's equations and the matching conditions imply either a nonlinear Hubble law or a very low large-scale density.