  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 Mpc/h. 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 Mpc/h 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 not in the observed sky and nor is 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 new
field of research in theoretical cosmology.
