Cosmological Gravitational Redshift and Hubble Tension

For almost a century since its first measurement by Hubble in 1929 the value of the Hubble constant, H, has been the subject of intense debate. In the last few years a new dimension has been added to this debate because there appears to be a significant discrepancy between the values of H derived from present-day universe (cepheids, supernova, lensed quasars, tip of the red giant branch), which are minimally dependent on cosmological theory and those derived from early universe observations (cosmic microwave background and baryon acoustic oscillations), which are based on the standard cosmological theory, ΛCDM , whereby ΛCDM in turn is based on the assumption that the universe is expanding. This discrepancy is known as Hubble tension. We resolve the Hubble tension by introducing a universe which is governed by the Taub-NUT solution to the field equations of general relativity. The Taub-NUT universe is not expanding. In this universe the observed cosmological redshift is due to the gravitational redshift associated with the Taub-Nut solution, which we refer to as cosmological gravitational redshift. Time dilation in this stationary universe has the same dependency on redshift, that generally has been seen as proof that space is expanding.