2022A&A...660A.139K

Context. 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 observations. Several previous studies claim that the homogeneity scale is reached at a radius around 70 h^–1 Mpc. However, the same observation shows a dramatic visual structure in the Sloan Digital Sky Survey Great Wall, which extends 300 h^–1 Mpc in linear dimension.
Aims. We present a homogeneity test for the matter distribution using the Baryon Oscillation Spectroscopic Survey Data Release 12 CMASS galaxy sample and clarify the ontological status of the CP.
Methods. As a homogeneity criterion, we compared 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) the direct estimation from the theoretical power spectrum.
Results. We show that the observed distribution is statistically impossible as a random distribution up to 300 h^–1 Mpc 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.
Conclusions. 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 the 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, which is a quadratic derivative of the metric.