From Fractal Cosmography to Fractal Cosmology

TL;DR

This paper explores the implications of assuming a fractal matter distribution in the universe, proposing a fractal cosmological model consistent with General Relativity and the Copernican Principle, and discussing its potential to clarify the universe's large-scale structure.

Contribution

It introduces a new fractal cosmological model based on the Conditional Cosmological Principle, extending standard cosmology to fractal distributions of matter.

Findings

The model aligns with the General Theory of Relativity and the Copernican Principle.

It offers a framework to test whether the universe is fractal or homogeneous at large scales.

The approach provides a basis for developing more realistic fractal universe models.

Abstract

Assuming a fractal distribution of matter in the universe, consequences that follow from the General Theory of Relativity and the Copernican Principle for fractal cosmology are examined. The change in perspective necessary to deal with a fractal universe is highlighted. An ansatz that provides a concrete application of the Conditional Cosmological Principle is provided. This fractal cosmology is obtained by arguments closely following those used in standard cosmology. The resulting model may play a significant role in the debate on whether the universe is a fractal or crosses over to homogeneity at some scale. This model may also be regarded as an idealized fractal model around which more realistic models may be built.