AbstractsAstronomy & Space Science

The current cosmological view asserts that the universe is homogeneous and isotropic; the observed heterogeneities are local in nature and should vanish at sufficiently large scales. This principle is based firstly on philosophical considerations: the observed universe must be statistically equal to any observer regardless of the point and direction of observation; and secondly, on cosmological observations: mainly isotropy measurements of the cosmic microwave background and clustering analysis of galaxies. This standard cosmological principle constitutes the basis of cosmology as a branch of physics. From the structure of space-time of the universe, to large-scale structure formation, this principle is present in the conceptual foundations, in the statistical information processes and the interpretation of the results. Regardless the success of the physical models based on the standard cosmological principle, there still remains unresolved fundamental questions within the formation of large scale structures in the universe. Is it supported by the observations the standard cosmological principle? And, What is scale of distance from which the homogeneity transition occurs? Already some research groups claim that astrophysical objects are grouped into highly structured hierarchical patterns with self-similarity properties, scale invariance and Hausdorff dimension less than the physical dimension of space, specific characteristics of fractal behaviour, where the standard cosmological principle is tested. Based on these concepts a topological analysis of large scale matter clustering in the universe is preformed from the fractal point of view. First is analysed the way in which dark matter is grouped at redshift z = 0 in the Millennium cosmological simulation. The determination of the homogeneity transition in the Millennium Simulation data is demonstrated from the behaviour of the fractal dimension and the lacunarity. The sliding window technique is used to determine the fractal mass-radius relation in order to find the fractal dimension, the pre-factor F and the lacunarity for the dark matter distribution in this simulation. In addition, the multi-fractal dimension and the lacunarity spectrum, including their dependence on a radial distance is obtained. These calculations demonstrate a radial distance dependency of all the fractal quantities, with heterogeneity clustering of dark matter haloes up to depths of 100 Mpc/h. Second, dark matter halo distribution is used in order to understand the fractal behaviour of the observed universe while avoiding the effects of luminosity selection. The data based on four limited-volume galaxy samples was obtained by Mu~noz-Cuartas & Mueller (2012) on the Seventh Data Release of the Sloan Digital Sky Survey (SDSS-DR7). In order to know the fractal behaviour of the observed universe, from the initial sample which contains 412468 galaxies, 339505 dark matter haloes were used as input the fractal calculations. Using again the sliding-window…