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The cosmological principle (CP), assuming spatially homogeneous and isotropicbackground geometry in the cosmological scale, is a fundamental assumption inmodern cosmology. Recent observations of the galaxy redshift survey providerelevant data to confront the principle with observation. We present ahomogeneity test for the matter distribution using the BOSS DR12 CMASS galaxysample and clarify the ontological status of the CP. As a homogeneitycriterion, we compare the observed data with similarly constructed randomdistributions using the number count in the truncated cones method. Comparisonsare also made with three theoretical results using the same method: (i) thedark matter halo mock catalogs from the N-body simulation, (ii) the log-normaldistributions derived from the theoretical matter power spectrum, and (iii)direct estimation from the theoretical power spectrum. We show that theobserved distribution is statistically impossible as a random distribution upto 300 Mpc/h in radius, which is around the largest statistically availablescale. However, comparisons with the three theoretical results show that theobserved distribution is consistent with these theoretically derived resultsbased on the CP. We show that the observed galaxy distribution (light) and thesimulated dark matter distribution (matter) are quite inhomogeneous even on alarge scale. Here, we clarify that there is no inconsistency surrounding theontological status of the CP in cosmology. In practice, the CP is applied tothe metric and the metric fluctuation is extremely small in all cosmologicalscales. This allows the CP to be valid as the averaged background in metric.The matter fluctuation, however, is decoupled from the small nature of metricfluctuation in the subhorizon scale. What is directly related to the matter inEinstein's gravity is the curvature, a quadratic derivative of the metric.

CMASS galaxy sample and the ontological status of the cosmological principle