Relativistic Fractal Cosmologies
  This article reviews an approach for constructing a simple relativistic
fractal cosmology whose main aim is to model the observed inhomogeneities of
the distribution of galaxies by means of the Lemaitre-Tolman solution of
Einstein's field equations for spherically symmetric dust in comoving
coordinates. This model is based on earlier works developed by L. Pietronero
and J.R. Wertz on Newtonian cosmology, whose main points are discussed.
Observational relations in this spacetime are presented, together with a
strategy for finding numerical solutions which approximate an averaged and
smoothed out single fractal structure in the past light cone. Such fractal
solutions are shown, with one of them being in agreement with some basic
observational constraints, including the decay of the average density with the
distance as a power law (the de Vaucouleurs' density power law) and the fractal
dimension in the range 1 <= D <= 2. The spatially homogeneous Friedmann model
is discussed as a special case of the Lemaitre-Tolman solution, and it is found
that once we apply the observational relations developed for the fractal model
we find that all Friedmann models look inhomogeneous along the backward null
cone, with a departure from the observable homogeneous region at relatively
close ranges. It is also shown that with these same observational relations the
Einstein-de Sitter model can have an interpretation where it has zero global
density, a result consistent with the "zero global density postulate" advanced
by Wertz for hierarchical cosmologies and conjectured by Pietronero for fractal
cosmological models. The article ends with a brief discussion on the possible
link between this model and nonlinear and chaotic dynamics.
