Top of the Cosmic Ladder and an Inquire on the Hubble Tension: on extragalactic distances and the evolution of Hubble Constant

The precise estimation of the Hubble Constant remains an open problem in observational astronomy and cosmology. Recent measurements of it based on the Cosmic Microwave Background (CMB) disagree with those from the local cosmic distance ladder (using Cepheids and Type Ia Supernovae), giving rise to the Hubble Tension. The estimation of the Hubble Constant rests upon how precise are the measurements for both the recession velocity and the distance to an object, being the latter the more challenging. Thus, this research develops a cosmological-model-independent method to estimate extragalactic distances, extending the distance ladder up to the order of Gigaparsecs. I then apply this method to estimate the distances to Active Galactic Nuclei (AGNs) in the GAIA's MILLIQUAS dataset, and use them to estimate the Hubble Constant in the present and its past evolution. From different estimation methods, I preliminarily find evidence of a time-varying Hubble Constant and an accelerating universe expansion. In particular, Local Universe measurements lead to values of the Hubble Constant that agree with Type Ia Supernovae and Tip of the Red Giant Branch estimations; while higher redshift measurements go closer to estimations using CMB.