Top of the Cosmic Ladder: On Extragalactic Distances and the Hubble Tension

The accurate determination of the Hubble parameter remains an open problem in modern cosmology. In recent investigations, conflicting measurements of its present value (the Hubble Constant) have arisen from the analysis of the Cosmic Microwave Background and estimations from the cosmic distance ladder, leading to the emergence of the Hubble tension. The primary issue with the latter method lies in the measurement of distances to distant objects, while the former approach is highly dependent on the cosmological model. This study introduces a new global-cosmology-independent technique, named the ``Hubble-Chains Method'', for estimating extragalactic distances. Leveraging the Pantheon+ catalog of 1700 Type Ia Supernovae, we employ this method to estimate the distances to ~10^5 radiosources from Gaia's MILLIQUAS catalog. Our findings reveal a redshift-dependent Hubble Parameter, suggesting an accelerating expansion of the Universe. Moreover, over different specifications, we can estimate the Hubble Constant to be 68.14+-0.24 km / s / Mpc under flat Lambda-CDM, and 68.42+-0.40 km / s / Mpc under Phantom wCDM, consistent with Universe ages of 13.646+-0.048 Gy and 13.648+0.079-0.080 Gy, respectively. In regard to the Hubble Tension, these results are inconsistent with Pantheon+ and SH0ES estimates for the local Universe, however, they are with measurements from the CMB. We also tested for non-uniformity in the expansion of the Universe and found no evidence contradicting the Cosmological Principle. Further investigations employing this methodology and data involve the refinement of cosmological models, Dark Energy parameter constraints, and testing the Lambda-CDM model.