The Evolving Baryonic Tully Fisher Relation: A Universal Law from Galaxies to Galactic Clusters (2511.20188v1)

Abstract: The Baryonic Tully - Fisher relation (BTFR) links the baryonic mass of galaxies to their characteristic rotational velocity and has been shown to with remarkable precision across a wide mass range. Recent studies, however, indicate that galaxy clusters occupy a parallel but offset relation, raising questions about the universality of the BTFR. Here, we demonstrate that the offset between galaxies and clusters arises naturally from cosmic time evolution. Using the evolving BTFR derived from the Nexus Paradigm of quantum gravity, we show that the normalization of the relation evolves as an exponential function of cosmic time., while the slope remains fixed at $\sim 4$. This provides a simple and predictive framework in which both galaxies and clusters obey the same universal scaling law, with their apparent offset reflecting their different formation epochs. Our results unify mass- velocity scaling across five orders of magnitude in baryonic mass, offering new insights into cosmic structure formation.