CMASS galaxy sample and the ontological status of the cosmological
  principle
  The cosmological principle (CP), assuming spatially homogeneous and isotropic
background geometry in the cosmological scale, is a fundamental assumption in
modern cosmology. Recent observations of the galaxy redshift survey provide
relevant data to confront the principle with observation. We present a
homogeneity test for the matter distribution using the BOSS DR12 CMASS galaxy
sample and clarify the ontological status of the CP. As a homogeneity
criterion, we compare the observed data with similarly constructed random
distributions using the number count in the truncated cones method. Comparisons
are also made with three theoretical results using the same method: (i) the
dark matter halo mock catalogs from the N-body simulation, (ii) the log-normal
distributions derived from the theoretical matter power spectrum, and (iii)
direct estimation from the theoretical power spectrum. We show that the
observed distribution is statistically impossible as a random distribution up
to 300 Mpc/h in radius, which is around the largest statistically available
scale. However, comparisons with the three theoretical results show that the
observed distribution is consistent with these theoretically derived results
based on the CP. We show that the observed galaxy distribution (light) and the
simulated dark matter distribution (matter) are quite inhomogeneous even on a
large scale. Here, we clarify that there is no inconsistency surrounding the
ontological status of the CP in cosmology. In practice, the CP is applied to
the metric and the metric fluctuation is extremely small in all cosmological
scales. This allows the CP to be valid as the averaged background in metric.
The matter fluctuation, however, is decoupled from the small nature of metric
fluctuation in the subhorizon scale. What is directly related to the matter in
Einstein's gravity is the curvature, a quadratic derivative of the metric.
