We test for reliability any signatures of field galaxies clustering in the GRB 021004 line of sight. The first signature is the GRB 021004 field photometric redshifts distribution based on the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences observations with a peak near z = 0.56 estimated from multicolor photometry in the GRB direction. The second signature is the Mg II 2796, 2803AA absorption doublet at z = 0.56 in VLT/UVES spectra obtained for the GRB 021004 afterglow. The third signature is the galaxy clustering in a larger (of about 3 sq.deg.) area around GRB 021004 with an effective peak near z = 0.56 for both the spectral and photometric redshifts from a few catalogs of clusters based on the Sloan Digital Sky Survey (SDSS) and Baryon Oscillation Spectroscopic Survey (BOSS) as a part of SDSS-III. From catalog data the size of the whole inhomogeneity in distribution of the galaxy cluster with the peak near z = 0.56 was also estimated as about 6--8 deg. or 140--190 Mpc. A possibility of inhomogeneity (a galaxy cluster) near the GRB 021004 direction can be also confirmed by an inhomogeneity in cosmic microwave background related with the Sunyaev-Zeldovich effect.

23 pages, 13 figures