Determination of the abundance of cosmic matter via the cell count
  moments of the galaxy distribution (1)
  We demonstrate that accurate and precise information about the matter content
of the universe can be retrieved via a simple cell count analysis of the 3D
spatial distribution of galaxies. A new clustering statistic, the {\it galaxy
clustering ratio} $\eta$, is the key in this process. This is defined as the
ratio between one- and two-point second-order moments of the smoothed galaxy
density distribution. The distinguishing feature of this statistic is its
universality: on large cosmic scales both galaxies (in redshift space) and mass
(in real space) display the same $\eta$ amplitude. This quantity, in addition,
does not evolve as a function of redshift. As a consequence, the $\eta$
statistic provides insight into characteristic parameters of the real-space
power spectrum of mass density fluctuations without the need to specify the
galaxy biasing function, a model for galaxy redshift distortions nor the
growing mode of density ripples. We demonstrate the method with the luminous
red galaxy (LRG) sample extracted from the spectroscopic Sloan Digital Sky
Survey (SDSS) data release 7 (DR7) catalogue. Taking weak (flat) priors of the
curvature of the universe ($\Omega_k$) and of the constant value of the dark
energy equation of state ($w$), and strong (gaussian) priors of the physical
baryon density $\Omega_bh^2$, of the Hubble constant $H_0$ and of the spectral
index of primordial density perturbations $n_s$, we estimate the abundance of
matter with a relative error of 8% ($\Omega_m= 0.283\pm0.023$). We expect that
this approach will be instrumental in searching for evidence of new physics
beyond the standard model of cosmology and in planning future redshift surveys
such as BigBOSS or EUCLID.
