Related papers: Scale Invariance in a Perturbed Einstein-de Sitter…
This paper presents an analysis of the smoothness problem in cosmology by focussing on the ambiguities originated in the simplifying hypotheses aimed at observationally verifying if the large-scale distribution of galaxies is homogeneous,…
This short communication advances the hypothesis that the observed fractal structure of large-scale distribution of galaxies is due to a geometrical effect, which arises when observational quantities relevant for the characterization of a…
The two-point correlation function for the dust distribution in the unperturbed Einstein-de Sitter cosmological model is studied along the past light cone. It was found that this function seems unable to represent the theoretical…
It is shown that density fluctuations obey a scaling law in an open Friedmann universe. In a flat universe, the fluctuations are not scale-invariant. We compute the growth rate of adiabatic scale-invariant density fluctuations in flat, open…
The large scale distribution of galaxies in the universe displays a complex pattern of clusters, super-clusters, filaments and voids with sizes limited only by the boundaries of the available samples. A quantitative statistical…
In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…
Counts of galaxies as a function of apparent magnitude are among the most time-honored observations in cosmology. In this Letter, we focus on some statistical properties of these counts which are fundamental in order to characterize the…
The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…
Nonlinear perturbations of Friedmann-Lemaitre cosmologies with dust and a positive cosmological constant have recently attracted considerable attention. In this paper our first goal is to compare the evolution of the first and second order…
We constructed a simple cosmological model which approximates the Einstein-de Sitter background with periodically distributed dust inhomogeneities. By taking the metric as a power series up to the third order in some perturbative parameter…
We use de Vaucouleurs' power-law density-distance relation, to study a hierarchical perturbation of the Friedmann universe. We solve the Einstein equation and obtain the density contrast and the amplification factor for the perturbation. It…
The effect of curvature on the results of fractal analyses of the galaxy distribution is investigated. We show that, if the universe satisfies the criteria of a wide class of parabolic homogeneous models, the observers measuring the fractal…
Two-point correlation function of galaxy distribution shows that the structure in the present Universe is scale-free up to a certain scale (at least several tens Mpc), which suggests that a fractal structure may exist. If small primordial…
Two fundamental empirical laws have been established in the analysis of galaxy space distribution. First, recent analyses have revealed that the three dimensional distribution of galaxies and clusters is characterized by large scale…
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…
Research done during the previous century established our Standard Cosmological Model. There are many details still to be filled in, but few would seriously doubt the basic premise. Past surveys have revealed that the large-scale…
While the universe becomes more and more homogeneous at large scales, statistical analysis of galaxy catalogs have revealed a fractal structure at small-scales (\lambda < 100 h^{-1} Mpc), with a fractal dimension D=1.5-2 (Sylos Labini et al…
I critically discuss in a pedagogical and phenomenological way a few crucial tests challenging the claims by Pietronero and collaborators that there is no evidence from available galaxy catalogues that the Universe is actually homogeneous…
The quantum model of homogeneous and isotropic universe filled with the uniform scalar field is considered. This model predicts effective inverse square-law dependence of the mean total energy density <\rho> on the expectation value of…
We revisit the {\it origin of structures problem} of standard Friedmann-Robertson-Walker cosmology to point out an unjustified approximation in the prevalent analysis. We follow common procedures in statistical mechanics to revise the issue…