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

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

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

Translocating the blood-brain barrier using electrostatics

Copyright © 2012 Ribeiro,Domingues, Freire,Santos and Castanho. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in other forums, provided the original authors and source are credited and subject to any copyright notices concerning any third-party graphics etc.Mammalian cell membranes regulate homeostasis, protein activity, and cell signaling. The charge at the membrane surface has been correlated with these key events. Although mammalian cells are known to be slightly anionic, quantitative information on the membrane charge and the importance of electrostatic interactions in pharmacokinetics and pharmacodynamics remain elusive. Recently, we reported for the first time that brain endothelial cells (EC) are more negatively charged than human umbilical cord cells, using zeta-potential measurements by dynamic light scattering. Here, we hypothesize that anionicity is a key feature of the blood-brain barrier (BBB) and contributes to select which compounds cross into the brain. For the sake of comparison, we also studied the membrane surface charge of blood components—red blood cells (RBC), platelets, and peripheral blood mononuclear cells (PBMC).To further quantitatively correlate the negative zeta-potential values with membrane charge density, model membranes with different percentages of anionic lipids were also evaluated. From all the cells tested, brain cell membranes are the most anionic and those having their lipids mostly exposed, which explains why lipophilic cationic compounds are more prone to cross the blood-brain barrier.Fundação para a Ciência e Tecnologia — Ministério da Educação e Ciência (FCT-MEC, Portugal) is acknowledged for funding (including fellowships SFRH/BD/42158/2007 to Marta M.B. Ribeiro, SFRH/BD/41750/2007 to Marco M. Domingues and SFRH/BD/70423/2010 to João M. Freire) and project PTDC/QUI-BIQ/119509/2010. Marie Curie Industry-Academia Partnerships and Pathways (European Commission) is also acknowledged for funding (FP7-PEOPLE-2007-3-1-IAPP, Project 230654)

The Apparent Fractal Conjecture: Scaling Features in Standard Cosmologies

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, and conjecturing that this distribution should follow a fractal pattern in perturbed standard cosmologies. This is due to a geometrical effect, appearing when certain types of average densities are calculated along the past light cone. The paper starts reviewing the argument concerning the possibility that the galaxy distribution follows such a scaling pattern, and the premises behind the assumption that the spatial homogeneity of standard cosmology can be observable. Next, it is argued that to discuss observable homogeneity one needs to make a clear distinction between local and average relativistic densities, and showing how the different distance definitions strongly affect them, leading the various average densities to display asymptotically opposite behaviours. Then the paper revisits Ribeiro's (1995: astro-ph/9910145) results, showing that in a fully relativistic treatment some observational average densities of the flat Friedmann model are not well defined at z ~ 0.1, implying that at this range average densities behave in a fundamentally different manner as compared to the linearity of the Hubble law, well valid for z < 1. This conclusion brings into question the widespread assumption that relativistic corrections can always be neglected at low z. It is also shown how some key features of fractal cosmologies can be found in the Friedmann models. In view of those findings, it is suggested that the so-called contradiction between the cosmological principle, and the galaxy distribution forming an unlimited fractal structure, may not exist.Comment: 30 pages, 2 figures, LaTeX. This paper is a follow-up to gr-qc/9909093. Accepted for publication in "General Relativity and Gravitation

Differential Density Statistics of Galaxy Distribution and the Luminosity Function

This paper uses data obtained from the galaxy luminosity function (LF) to calculate two types of radial number densities statistics of the galaxy distribution as discussed in Ribeiro (2005), namely the differential density $\gamma$ and the integral differential density $\gamma^\ast$. By applying the theory advanced by Ribeiro and Stoeger (2003), which connects the relativistic cosmology number counts with the astronomically derived LF, the differential number counts $dN/dz$ are extracted from the LF and used to calculate both $\gamma$ and $\gamma^\ast$ with various cosmological distance definitions, namely the area distance, luminosity distance, galaxy area distance and redshift distance. LF data are taken from the CNOC2 galaxy redshift survey and $\gamma$ and $\gamma^\ast$ are calculated for two cosmological models: Einstein-de Sitter and an $\Omega_{m_0}=0.3$, $\Omega_{\Lambda_0}=0.7$ standard cosmology. The results confirm the strong dependency of both statistics on the distance definition, as predicted in Ribeiro (2005), as well as showing that plots of $\gamma$ and $\gamma^\ast$ against the luminosity and redshift distances indicate that the CNOC2 galaxy distribution follows a power law pattern for redshifts higher than 0.1. These findings bring support to Ribeiro's (2005) theoretical proposition that using different cosmological distance measures in statistical analyses of galaxy surveys can lead to significant ambiguity in drawing conclusions about the behavior of the observed large scale distribution of galaxies.Comment: LaTeX, 37 pages, 6 tables, 10 figures. Accepted for publication in "The Astrophysical Journal