  This paper seeks to check the validity of the "apparent fractal conjecture"
(Ribeiro 2001ab: gr-qc/9909093, astro-ph/0104181), which states that the
observed power-law behaviour for the average density of large-scale
distribution of galaxies arises when some observational quantities, selected by
their relevance in average density profile determination, are calculated along
the past light cone. Implementing these conditions in the proposed set of
observational relations profoundly changes the behaviour of many observables in
the standard cosmological models. In particular, the average density becomes
observationally 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 decaying power-law like average density
profile, meaning that the dust distribution of this cosmology has a scaling
behaviour compatible with the power-law profile of the density-distance
correlation observed in the galaxy catalogues. These results show that, in the
context of this work, the apparent fractal conjecture is correct.
