Some models of the expanding Universe predict that the astrometric proper motion of distant radio sources embedded in space-time are non-zero as the radial distance from observer to the source grows. Systematic proper motion effects would produce a predictable quadrupole pattern on the sky that could be detected using Very Long Baseline Interferometry (VLBI) technique. This quadrupole pattern can be interpreted either as an anisotropic Hubble expansion, or as a signature of the primordial gravitational waves in the early Universe. We present our analysis of a large set of geodetic VLBI data spanning 1979--2015 to estimate the dipole and quadrupole harmonics in the expansion of the vector field of the proper motions of quasars in the sky. The analysis is repeated for different redshift zones.
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