26,992 research outputs found
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
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 . 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
, that may only happen in redshifts as low as , 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
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
The Apparent Fractal Conjecture
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 cosmological fractal structure are calculated along the
past light cone. If this hypothesis proves, even partially, correct, most, if
not all, objections raised against fractals in cosmology may be solved. For
instance, under this view the standard cosmology has zero average density, as
predicted by an infinite fractal structure, with, at the same time, the
cosmological principle remaining valid. The theoretical results which suggest
this conjecture are reviewed, as well as possible ways of checking its
validity.Comment: 6 pages, LaTeX. Text unchanged. Two references corrected. Contributed
paper presented at the "South Africa Relativistic Cosmology Conference in
Honour of George F. R. Ellis 60th Birthday"; University of Cape Town,
February 1-5, 199
Scale Invariance in a Perturbed Einstein-de Sitter Cosmology
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.Comment: 18 pages, 1 figure, LaTeX. Final version (small changes in the figure
plus some references update). Fortran code included with the LaTeX source. To
be published in "Fractals
Spatial and observational homogeneities of the galaxy distribution in standard cosmologies
This work discusses the possible empirical verification of the geometrical
concept of homogeneity of the standard relativistic cosmology considering its
various definitions of distance. We study the physical consequences of the
distinction between the usual concept of spatial homogeneity (SH), as defined
by the Cosmological Principle, and the concept of observational homogeneity
(OH), arguing that OH is in principle falsifiable by means of astronomical
observations, whereas verifying SH is only possible indirectly. Simulated
counts of cosmological sources are produced by means of a generalized
number-distance expression that can be specialized to produce either the counts
of the Einstein-de Sitter (EdS) cosmology, which has SH by construction, or
other types of counts, which do, or do not, have OH by construction.
Expressions for observational volumes and differential densities are derived
with the various cosmological distance definitions in the EdS model. Simulated
counts that have OH by construction do not always exhibit SH features. The
reverse situation is also true. Besides, simulated counts with no OH features
at low redshift start showing OH characteristics at high redshift. The comoving
distance seems to be the only distance definition where both SH and OH appear
simultaneously. The results show that observations indicating possible lack of
OH do not necessarily falsify the standard Friedmannian cosmology, meaning that
this cosmology will not necessarily always produce observable homogeneous
densities. The general conclusion is that the use of different cosmological
distances in the characterization of the galaxy distribution lead to
significant ambiguities in reaching conclusions about the behavior of the
large-scale galaxy distribution in the Universe.Comment: 12 pages, 12 figures, LaTeX. Matches the final version sent to the
journal. Accepted for publication in "Astronomy and Astrophysics
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