The cosmological principle is not in the sky

The homogeneity of matter distribution at large scales, known as the cosmological principle, is a central assumption in the standard cosmological model. The case is testable though, thus no longer needs to be a principle. Here we perform a test for spatial homogeneity using the Sloan Digital Sky Survey Luminous Red Galaxies (LRG) sample by counting galaxies within a specified volume with the radius scale varying up to 300 h⁻¹ Mpc. We directly confront the large-scale structure data with the definition of spatial homogeneity by comparing the averages and dispersions of galaxy number counts with allowed ranges of the random distribution with homogeneity. The LRG sample shows significantly larger dispersions of number counts than the random catalogues up to 300 h⁻¹ Mpc scale, and even the average is located far outside the range allowed in the random distribution; the deviations are statistically impossible to be realized in the random distribution. This implies that the cosmological principle does not hold even at such large scales. The same analysis of mock galaxies derived from the N-body simulation, however, suggests that the LRG sample is consistent with the current paradigm of cosmology, thus the simulation is also not homogeneous in that scale. We conclude that the cosmological principle is neither in the observed sky nor demanded to be there by the standard cosmological world model. This reveals the nature of the cosmological principle adopted in the modern cosmology paradigm, and opens a new field of research in theoretical cosmology.