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 st
andard 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.
We study the galaxy cosmological mass function (GCMF) in a semi-empirical relativistic approach using observational data provided by galaxy redshift surveys. Starting from the theory of Ribeiro & Stoeger (2003, arXiv:astro-ph/0304094) between the mas
s-to-light ratio, the selection function obtained from the luminosity function (LF) data and the luminosity density, the average luminosity $L$ and the average galactic mass $mathcal{M}_g$ are computed in terms of the redshift. $mathcal{M}_g$ is also alternatively estimated by a method that uses the galaxy stellar mass function (GSMF). Comparison of these two forms of deriving the average galactic mass allows us to infer a possible bias introduced by the selection criteria of the survey. We used the FORS Deep Field galaxy survey sample of 5558 galaxies in the redshift range $0.5 < z < 5.0$ and its LF Schechter parameters in the B-band, as well as this samples stellar mass-to-light ratio and its GSMF data. Assuming ${mathcal{M}_{g_0}} approx 10^{11} mathcal{M}_odot$ as the local value of the average galactic mass, the LF approach results in $L_{B} propto (1+z)^{(2.40 pm 0.03)}$ and $mathcal{M}_g propto (1+z)^{(1.1pm0.2)}$. However, using the GSMF results produces $mathcal{M}_g propto (1+z)^{(-0.58 pm 0.22)}$. We chose the latter result as it is less biased. We then obtained the theoretical quantities of interest, such as the differential number counts, to calculate the GCMF, which can be fitted by a Schechter function. The derived GCMF follows theoretical predictions in which the less massive objects form first, being followed later by more massive ones. In the range $0.5 < z < 2.0$ the GCMF has a strong variation that can be interpreted as a higher rate of galaxy mergers or as a strong evolution in the star formation history of these galaxies.
This paper studies the connection between the relativistic number density of galaxies down the past light cone in a Friedmann-Lemaitre-Robertson-Walker spacetime with non-vanishing cosmological constant and the galaxy luminosity function (LF) data. I
t extends the redshift range of previous results presented in Albani et al. (2007:astro-ph/0611032) where the galaxy distribution was studied out to z=1. Observational inhomogeneities were detected at this range. This research also searches for LF evolution in the context of the framework advanced by Ribeiro and Stoeger (2003:astro-ph/0304094), further developing the theory linking relativistic cosmology theory and LF data. Selection functions are obtained using the Schechter parameters and redshift parametrization of the galaxy luminosity functions obtained from an I-band selected dataset of the FORS Deep Field galaxy survey in the redshift range 0.5<z<5.0 for its blue bands and 0.75<z<3.0 for its red ones. Differential number counts, densities and other related observables are obtained, and then used with the calculated selection functions to study the empirical radial distribution of the galaxies in a fully relativistic framework. The redshift range of the dataset used in this work, which is up to five times larger than the one used in previous studies, shows an increased relevance of the relativistic effects of expansion when compared to the evolution of the LF at the higher redshifts. The results also agree with the preliminary ones presented in Albani et al. (2007:astro-ph/0611032), suggesting a power-law behavior of relativistic densities at high redshifts when they are defined in terms of the luminosity distance.
This work presents an empirical study of the evolution of the personal income distribution in Brazil. Yearly samples available from 1978 to 2005 were studied and evidence was found that the complementary cumulative distribution of personal income for
99% of the economically less favorable population is well represented by a Gompertz curve of the form $G(x)=exp [exp (A-Bx)]$, where $x$ is the normalized individual income. The complementary cumulative distribution of the remaining 1% richest part of the population is well represented by a Pareto power law distribution $P(x)= beta x^{-alpha}$. This result means that similarly to other countries, Brazils income distribution is characterized by a well defined two class system. The parameters $A$, $B$, $alpha$, $beta$ were determined by a mixture of boundary conditions, normalization and fitting methods for every year in the time span of this study. Since the Gompertz curve is characteristic of growth models, its presence here suggests that these patterns in income distribution could be a consequence of the growth dynamics of the underlying economic system. In addition, we found out that the percentage share of both the Gompertzian and Paretian components relative to the total income shows an approximate cycling pattern with periods of about 4 years and whose maximum and minimum peaks in each component alternate at about every 2 years. This finding suggests that the growth dynamics of Brazils economic system might possibly follow a Goodwin-type class model dynamics based on the application of the Lotka-Volterra equation to economic growth and cycle.
