Another cosmological redshift mechanism could exist in general relativity, as is differences in the global metric field gμν between the radiation source in the past, and the observer in the present, known as gravitational redshift in massive stars. In this paper, we present a fully conformal global metric model with time scaling that would lead to the above alternative interpretation of the cosmological redshift. It is based on a relatively simple global solution of Einstein's gravitational equations without the cosmological term, and the analysis also shows other interesting astrophysical implications. The model naturally solves the problem of critical density and spatial flatness, as well as the problem of cosmological redshift in the spectra of distant astrophysical sources, and the problem of Olbers' and Seeliger's paradox. At the same time, it replaces the strict causal horizon principle with a much softer formulation-the region of the practically observable universe. Confrontation with astrophysical data provides interesting agreement with the spatial distribution of astrophysical radiation sources such as γ-ray bursts and quasars. However, probably the most important consequence is the new, generalized formulation of Hubble's law z(r) = (exp(Hr/c)-1), which shows good agreement R 2 ≈ 0.9824 with experimental data even for very distant sources. The paper also physically justifies in principle the modification of Newton's law of gravity for infinite space proposed by Seeliger. The modifying exponential term exp(-Hr/c) is uniquely quantified by the Hubble parameter and the speed of light.