The scale of homogeneity of the galaxy distribution in SDSS DR6
  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 $70 h^{-1} {\rm Mpc}$.
