The scale of homogeneity of the galaxy distribution in SDSS DR6

TL;DR

This study uses multifractal analysis on SDSS DR6 data to determine the scale at which the galaxy distribution becomes homogeneous, finding it occurs between 60 and 70 h^{-1} Mpc, supporting the cosmological principle.

Contribution

It applies a multifractal analysis to SDSS DR6 data and simulations to precisely estimate the scale of homogeneity in the galaxy distribution.

Findings

Galaxy distribution becomes homogeneous between 60 and 70 h^{-1} Mpc.

Results are consistent with previous studies.

SDSS data aligns with random homogeneous samples at large scales.

Abstract

The assumption that the Universe, on sufficiently large scales, is homogeneous and isotropic is crucial to our current understanding of cosmology. In this paper we test if the observed galaxy distribution is actually homogeneous on large scales. We have carried out a multifractal analysis of the galaxy distribution in a volume limited subsample from the SDSS DR6. This considers the scaling properties of different moments of galaxy number counts in spheres of varying radius $r$ centered on galaxies. This analysis gives the spectrum of generalized dimension $D_q(r)$, where $q >0$ quantifies the scaling properties in overdense regions and $q<0$ in underdense regions. We expect $D_q(r)=3$ for a homogeneous, random point distribution. In our analysis we have determined $D_q(r)$ in the range $-4 \le q \le 4$ and $7 \le r \le 98 h^{-1} {\rm Mpc}$. In addition to the SDSS data we have analysed several random samples which are homogeneous by construction. Simulated galaxy samples generated from dark matter N-body simulations and the Millennium Run were also analysed. The SDSS data is considered to be homogeneous if the measured $D_q$ is consistent with that of the random samples. We find that the galaxy distribution becomes homogeneous at a length-scale between 60 and $70 h^{-1} {\rm Mpc}$. The galaxy distribution, we find, is homogeneous at length-scales greater than $70 h^{-1} {\rm Mpc}$. This is consistent with earlier works which find the transition to homogeneity at around $70 h^{-1} {\rm Mpc}$.