Dark energy and statistical formalisms for large structure formation

• Grant number: 07/00036-4
• Support Opportunities: Scholarships in Brazil - Post-Doctorate
• Effective date (Start): January 01, 2008
• Effective date (End): February 14, 2009
• Field of knowledge: Physical Sciences and Mathematics - Astronomy - Extragalactic Astrophysics
• Principal Investigator: Jose Ademir Sales de Lima
• Grantee: Lucio Marassi de Souza Almeida
• Host Institution: Instituto de Astronomia, Geofísica e Ciências Atmosféricas (IAG). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The present project is focused on the mysterious nature of the dark components of the universe (dark matter and dark energy) and their consequences for the process of formation of the large structures of the universe (galaxies, clusters and superclusters of galaxies).The process of structure formation was analytically described by Press and Schechter in 1974, through the mass function, F(M), or multiplicity function of the galaxy clusters. This function determines the comoving numerical density of gravitationally bound objects that are formed during the process. The so-called Press-Schechter formalism has as starting point the hypothesis that the statistics of the primordial density perturbation field is well described by a Gaussian distribution. Besides a serious normalization problem (when integrating dF(M) over all masses we obtain 1/2), that method does not explain the current X-ray data from galaxy clusters, and it is also in disagreement with the most modern numerical simulations.In this context, we propose in this project a more detailed study of the statistics used to describe the density perturbation field, since the most recent data of WMAP (Spergel et al. 2006, Hinshaw et al. 2007) indicate a deviation from gaussianity in the cosmic background radiation maps. Our starting point is that the probable deviations of the Gaussian distribution might be due to the correlations induced by the cosmic gravitational field itself. As it happens in the dynamics of galaxies and clusters (Lima and de Souza 2005, Kronberger et al. 2006), such deviations can be described by the nonextensive statistics of Tsallis (1988). This special emphasis in the nonextensive statistics is also justified by the fact that it allows a semi-analytical treatment which reduces to a Gaussian distribution when its free parameter q goes to unity, thereby making possible a direct comparison with the results of the standard theory.Of course, other distributions will also be studied considering the most recent available data. The idea is to establish the distributions that correct the normalization problem, and at the same time provide better fits with the X-ray spectrum data from clusters. In that sense, we should accomplish a wide comparison of the modified mass functions (by the different statistics) with the data of several catalogs of galaxies and fits from recent N-body simulations. The mass functions and, implicitly, the distributions describing the field of primordial fluctuations will be tested in several cosmological scenarios, including the different types of dark energy proposed in the literature. The main goal (in the non-gaussian point of view) is to obtain constraints over several cosmic parameters of the structure formation of the universe. (AU)