Statistical characteristics of large scale structure^*

¹ Institute of Theoretical Physics, University of Warsaw, 00-681 Warsaw, Poland
² Department of Astronomy, Williams College, Williamstown, MA 01267, USA
³ Theoretical Astrophysics Center, Juliane Maries Vej 30, 2100 Copenhagen Ø, Denmark e-mail: dorr@tac.dk
⁴ Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047 Moscow, Russia

Received: 2 May 2003
Accepted: 19 April 2004

Abstract

We generalize and extend the statistical description of formation and evolution of Large Scale matter distribution in the Universe proposed in our previous papers. We investigate the impact of transverse motions – expansion and/or compression – on properties of the Large Scale Structure elements – walls, pancakes, filaments and clouds – and, generalizing the Press-Schechter formalism, derive their mass functions. Using the Zel'dovich theory of gravitational instability we show that these mass functions are approximately the same and the mass of each type of elements is found to be concentrated near the corresponding mean mass. At high redshifts, both the mass function and the mean mass of formed elements depend upon the small scale part of the initial power spectrum and, in particular, upon the mass of dominant fraction of dark matter (DM) particles. Using these results we obtain independent estimates of probable redshifts of the reionization and reheating periods of the Universe. We show that the transverse motions do not significantly change the redshift evolution of the observed mass function and the mean linear number density of low mass pancakes related to absorption lines in the spectra of the farthest quasars. Application of this approach to the observed Lyman–α forest allows one to directly estimate the shape of initial power spectrum on small scales.