The scale of homogeneity of the galaxy distribution in SDSS DR6

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 $70 h^{-1} {\rm Mpc}$.Comment: 6 pages, 3 figures, Submitted for publicatio

A giant ring-like structure at 0.78 < z < 0.86 displayed by GRBs

“…Bagla, Yadav & Seshadri (2008) showed that in the concordance model, the fractal dimension makes a rapid transition to values close to 3 at scales between 40 and 100 Mpc. Sarkar et al (2009) found the galaxy distribution to be homogeneous at length-scales greater than 70 h −1 Mpc, and Yadav, Bagla & Khandai (2010) estimated the upper limit to the scale of homogeneity as being close to 260 h −1 Mpc for the ΛCDM model. Söchting et al (2012) studied the Ultra Deep Catalogue of Galaxy Structures; the cluster catalogue contains 1780 structures covering the redshift range 0.2 < z < 3.0, spanning three orders of magnitude in luminosity (10 8 < L4 < 5 × 10 11 L⊙) and richness from eight to hundreds of galaxies.…”

Homogeneity and isotropy in the Two Micron All Sky Survey Photometric Redshift catalogue

“…The most commonly used of them is the so-called correlation dimension D2(r), which quantifies the filling factor of spheres of different radii centred on points in the distribution. Using this kind of observables, different groups have been able to measure the transition from a fractal with D2 < 3 to a homogeneous distribution D2 = 3 on scales rH ∼ 100 Mpc (Guzzo 1997;Pan & Coles 2000;Kurokawa et al 2001;Hogg et al 2005;Seshadri 2005;Sarkar et al 2009;Scrimgeour et al 2012;Nadathur 2013), while other authors claim that such transition has not yet been observed (Joyce et al 1999(Joyce et al , 2005Sylos Labini 2011a,b;Sylos Labini et al 2014). In order to perform such analyses, full three-dimensional information for all the galaxies is necessary, and therefore these methods have only been used on spectroscopic catalogues, which traditionally cover much smaller volumes than their photometric counterparts.…”

Exact nonlinear inhomogeneities inΛCDMcosmology

“…It turns out that, within very special models, one can even eliminate Λ entirely, for instance for observers near the center of a spherically symmetric model (see [37] and references therein). However, it is an open question whether this can be achieved in inhomogeneous models which exhibit an average homogeneity on the scales on which it seems to be observed [10], i.e. models in which the cosmological principle is preserved.…”

“…Even if it becomes homogeneous above a certain scale (see e.g. [10]), the size of this "fair sample" [2] depends on how we measure it and what we mean by "statistical homogeneity" (cf. [11] and [12] for alternative views).…”