Observations in the Einstein--de Sitter Cosmology: Dust Statistics and Limits of Apparent Homogeneity

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 distribution of dust along the backward null cone of this unperturbed model, which has already been determined in a previous paper as being apparently inhomogeneous at ranges usually considered as local. Such result was revisited in order to determine more precisely the quantitative limits where, in theory, we can detect apparent homogeneity, and it was found that this may only happen up to $z \sim 10^{-2}$. A different statistical analysis proposed by Pietronero is used, and it appears to be able to represent more accurately the theoretical distribution of dust in this cosmology. In the light of these results, it is argued that the usual practice of disregarding relativistic effects in studies of distribution of galaxies, by considering them as being placed on local regions, seems to be valid only on much closer scales than it is commonly believed. In the Einstein-de Sitter cosmology with $H_0=75 km s^{-1} Mpc^{-1}$, that may only happen in redshifts as low as $z \approx 0.04$, which means that the local approximation seems to be valid up to zeroth order of approximation only. As at present there are many redshift surveys which have already probed at deeper ranges, it seems that in order to compare the Friedmann models with observations we have to be very careful when ignoring the past light cone problem in observational cosmology, either in theoretical calculations or in data analysis, due to relativistic effects which produce observable inhomogeneity even in spatially homogeneous cosmological models.Comment: standard LaTeX; 23 pages, 2 tables, 3 LaTeX figures; paper published in 1995 is archived her

Cosmological Distances and Fractal Statistics of Galaxy Distribution

This paper studies the effect of the distance choice in radial (non-average) statistical tools used for fractal characterization of galaxy distribution. After reviewing the basics of measuring distances of cosmological sources, various distance definitions are used to calculate the differential density $\gamma$ and the integral differential density $\gamma^\ast$} of the dust distribution in the Einstein-de Sitter cosmology. The main results are as follows: (1) the choice of distance plays a crucial role in determining the scale where relativistic corrections must be taken into account, as both $\gamma$ and $\gamma^\ast$ are strongly affected by such a choice; (2) inappropriate distance choices may lead to failure to find evidence of a galaxy fractal structure when one calculates those quantities, even if such a structure does occur in the galaxy distribution; (3) the comoving distance and the distance given by Mattig's formula are unsuitable to probe for a possible fractal pattern as they render $\gamma$ and $\gamma^\ast$ constant for all redshifts; (4) a possible galaxy fractal system at scales larger than 100Mpc (z \~ 0.03) may only be found if those statistics are calculated with the luminosity or redshift distances, as they are the ones where $\gamma$ and $\gamma^\ast$ decrease at higher redshifts; (5) C\'el\'erier and Thieberger's (2001) critique of Ribeiro's (1995: astro-ph/9910145) earlier study are rendered impaired as their objections were based on misconceptions regarding relativistic distance definitions.Comment: 14 pages, 4 figures, A&A LaTeX macro. Minor linguistic changes to match the version sent to the publisher. Accepted for publication in "Astronomy and Astrophysics

A Fortran Code for Null Geodesic Solutions in the Lemaitre-Tolman-Bondi Spacetime

This paper describes the Fortran 77 code SIMU, version 1.1, designed for numerical simulations of observational relations along the past null geodesic in the Lemaitre-Tolman-Bondi (LTB) spacetime. SIMU aims at finding scale invariant solutions of the average density, but due to its full modularity it can be easily adapted to any application which requires LTB's null geodesic solutions. In version 1.1 the numerical output can be read by the GNUPLOT plotting package to produce a fully graphical output, although other plotting routines can be easily adapted. Details of the code's subroutines are discussed, and an example of its output is shown.Comment: 13 pages, 10 figures, LaTeX. Fortran code included with the LaTeX source code (also available at http://www.if.ufrj.br/~mbr/codes). Accepted for publication in "Computer Physics Communications

Dogmatism and Theoretical Pluralism in Modern Cosmology

This work discusses the presence of a dogmatic tendency within modern cosmology, and some ideas capable of neutralizing its negative influence. It is verified that warnings about the dangers of dogmatic thinking in cosmology can be found as early as the 1930's, and we discuss the modern appearance of "scientific dogmatism". The solution proposed to counteract such an influence, which is capable of neutralizing this dogmatic tendency, has its origins in the philosophical thinking of the Austrian physicist Ludwig Boltzmann (1844-1906). In particular we use his two main epistemological theses, scientific theories as representations of nature and theoretical pluralism, to show that once they are embodied in the research practice of modern cosmology, there is no longer any reason for dogmatic behaviours.Comment: 14 pages; LaTeX sourc

Boltzmann's Concept of Reality

In this article we describe and analyze the concept of reality developed by the Austrian theoretical physicist Ludwig Boltzmann. It is our thesis that Boltzmann was fully aware that reality could, and actually was, described by different points of view. In spite of this, Boltzmann did not renounce the idea that reality is real. We also discuss his main motivations to be strongly involved with philosophy of science, as well as further developments made by Boltzmann himself of his main philosophical ideas, namely scientific theories as images of Nature and its consequences. We end the paper with a discussion about the modernity of Boltzmann's philosophy of science.Comment: 13 pages, pdf only. To appear in the book on Ludwig Boltzmann scientific philosophy, published by Nova Science. Edited by A. Eftekhar

Fractal analysis of the galaxy distribution in the redshift range 0.45 < z < 5.0

Evidence is presented that the galaxy distribution can be described as a fractal system in the redshift range of the FDF galaxy survey. The fractal dimension $D$ was derived using the FDF galaxy volume number densities in the spatially homogeneous standard cosmological model with $\Omega_{m_0}=0.3$, $\Omega_{\Lambda_0}=0.7$ and H_0=70 \; \mbox{km} \; {\mbox{s}}^{-1} \; {\mbox{Mpc}}^{-1}. The ratio between the differential and integral number densities $\gamma$ and $\gamma^\ast$ obtained from the red and blue FDF galaxies provides a direct method to estimate $D$, implying that $\gamma$ and $\gamma^\ast$ vary as power-laws with the cosmological distances. The luminosity distance $d_{\scriptscriptstyle L}$, galaxy area distance $d_{\scriptscriptstyle G}$ and redshift distance $d_z$ were plotted against their respective number densities to calculate $D$ by linear fitting. It was found that the FDF galaxy distribution is characterized by two single fractal dimensions at successive distance ranges. Two straight lines were fitted to the data, whose slopes change at $z \approx 1.3$ or $z \approx 1.9$ depending on the chosen cosmological distance. The average fractal dimension calculated using $\gamma^\ast$ changes from $\langle D \rangle=1.4^{\scriptscriptstyle +0.7}_{\scriptscriptstyle -0.6}$ to $\langle D \rangle=0.5^{\scriptscriptstyle +1.2}_{\scriptscriptstyle -0.4}$ for all galaxies, and $D$ decreases as $z$ increases. Small values of $D$ at high $z$ mean that in the past galaxies were distributed much more sparsely and the large-scale galaxy structure was then possibly dominated by voids. Results of Iribarrem et al. (2014, arXiv:1401.6572) indicating similar fractal features with $\langle D \rangle =0.6 \pm 0.1$ in the far-infrared sources of the Herschel/PACS evolutionary probe (PEP) at $1.5 \lesssim z \lesssim 3.2$ are also mentioned.Comment: LaTex, 15 pages, 28 figures, 4 tables. To appear in "Physica A