Fractality in a Perturbed Einstein-de Sitter Cosmology

This paper seeks to check the validity of a hypothesis known as the “apparent fractal conjecture” (Ribeiro 1999: gr-qc/9909093), which states that the observed fractal structure of large-scale distribution of galaxies arises when some observational quantities, selected by their relevance in fractal characterization, are calculated along the past light cone. Since general relativity states that astronomical observations are carried out in this spacetime hypersurface, observables necessary for direct comparison with astronomical data must be calculated along it. Implementing this condition in the proposed set of observational relations profoundly changes the behaviour of many observables in the standard cosmological models. In particular, the observed average density becomes inhomogeneous, even in the spatially homogeneous spacetime of standard cosmology, change which was already analysed by Ribeiro (1992b, 1993, 1994, 1995: astro-ph/9910145) for a non-perturbed model. Here we derive observational relations in a perturbed Einstein-de Sitter cosmology by means of the perturbation scheme proposed by Abdalla and Mohayaee (1999: astro-ph/9810146), where the scale factor is expanded in power series to yield perturbative terms. The differential equations derived in this perturbative context, and other observables necessary in our analysis, are solved numerically. The results show that our perturbed Einstein-de Sitter cosmology can be approximately described by a fractal like distribution, meaning that the dust distribution of this cosmology has a scaling behaviour compatible with an observable single fractal system. These results show that, in the context of this work, the apparent fractal conjecture is correct. Subject headings: cosmology: theory