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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
and the integral differential density } 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
and 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 and 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 and
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
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 was derived using the FDF galaxy volume number densities in the
spatially homogeneous standard cosmological model with ,
and H_0=70 \; \mbox{km} \; {\mbox{s}}^{-1} \;
{\mbox{Mpc}}^{-1}. The ratio between the differential and integral number
densities and obtained from the red and blue FDF
galaxies provides a direct method to estimate , implying that and
vary as power-laws with the cosmological distances. The
luminosity distance , galaxy area distance
and redshift distance were plotted against
their respective number densities to calculate 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 or depending on
the chosen cosmological distance. The average fractal dimension calculated
using changes from to for all galaxies, and decreases as
increases. Small values of at high 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 in the far-infrared sources of the Herschel/PACS evolutionary
probe (PEP) at are also mentioned.Comment: LaTex, 15 pages, 28 figures, 4 tables. To appear in "Physica A
Direito Internacional
Divulgação dos SUMÁRIOS das obras recentemente incorporadas ao acervo da Biblioteca
Ministro Oscar Saraiva do STJ. Em respeito à lei de Direitos Autorais, não disponibilizamos a
obra na íntegra.Localização na estante: 341.1/.8 U17
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