On Modelling a Relativistic Hierarchical (Fractal) Cosmology by Tolman's Spacetime. II. Analysis of the Einstein-de Sitter Model

TL;DR

This paper analyzes the Einstein-de Sitter cosmological model within a relativistic hierarchical framework, examining its fractal properties and homogeneity along the past light cone, and finds it lacks fractal features.

Contribution

It demonstrates how the Einstein-de Sitter model can be viewed as a special case of Lemaitre-Tolman's spacetime and investigates its fractal behavior observationally.

Findings

The model does not remain homogeneous along the geodesic.

It exhibits no fractal features along the backward null cone.

Abstract

This paper studies the spatially homogeneous Einstein-de Sitter cosmological model in the context of a relativistic hierarchical (fractal) cosmology as developed in paper I (0807.0866). The Einstein-de Sitter model is treated as a special case of Lemaitre-Tolman's spacetime, obtained by the appropriate choice of the latter's three arbitrary functions. The observational relations along the past light cone of the model under consideration are calculated, and an investigation of whether or not it has fractal behaviour is performed. It was found that the Einstein-de Sitter model does not seem to remain homogeneous along the geodesic and that it also has no fractal features along the backward null cone.