Absence of self-averaging and of homogeneity in the large-scale galaxy distribution

¹  Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi - Piazzale del Viminale 1, 00184 Rome, Italy, EU
²  Istituto dei Sistemi Complessi CNR - Via dei Taurini 19, 00185 Rome, Italy, EU
³  Institute of Astronomy, St. Petersburg State University - Staryj Peterhoff, 198504, St. Petersburg, Russia
⁴  Dipartimento di Fisica, Università di Roma “Sapienza” - Piazzale Aldo Moro 2, 00185 Rome, Italy, EU

Corresponding author: Francesco.SylosLabini@roma1.infn.it

Received: 6 April 2009
Accepted: 24 April 2009

Abstract

The properties of the galaxy distribution at large scales are usually studied using statistics which are assumed to be self-averaging inside a given sample. We present a new analysis able to quantitatively map galaxy large-scale structures while testing for the stability of average statistical quantities in different sample regions. We find that the newest samples of the Sloan Digital Sky Survey provide unambiguous evidence that galaxy structures correspond to large-amplitude density fluctuations at all scales limited only by sample sizes. The two-point correlations properties are self-averaging up to approximately 30 Mpc/h and are characterized by a fractal dimension D = 2.1±0.1. Then at all larger scales probed density fluctuations are too large in amplitude and too extended in space to be self-averaging inside the considered volumes. These inhomogeneities are compatible with a continuation of fractal correlations but incompatible with: i) a homogeneity scale smaller than 100 Mpc/h, ii) predictions of standard theoretical models, iii) mock galaxy catalogs generated from cosmological N-body simulations.