Phenomenology of renormalization group improved gravity from the kinematics of SPARC galaxies

Renormalization Group correction to General Relativity (RGGR) proposes a logarithmic running of the gravitational coupling $\left(G\right)$, resulting in a modified description of gravity. This has the potential to explain the observed kinematics of the galaxies, including the missing-mass problem. We, for the first time, based on the galaxy morphological types, investigate the dynamics of a diverse collection of galaxies present in the Spitzer Photometry for Accurate Rotation Curve (SPARC) catalog. We phenomenologically constrain the RGGR model parameter $\left(\bar\nu\right)$ along with the mass-to-light ratio for a sample of 100 SPARC galaxies, selected from four different morphological types, viz. early, spiral, late, and starburst. Our statistical analysis finds RGGR to fit the observed galaxy kinematics consistently. The constrained RGGR model parameter also supports the claim that it has a near-linear dependence on the galactic baryonic mass. From our morphology study, we find that the parameter $\bar\nu$ decreases from the early-type to the starburst galaxies. Finally, the renormalization group improved gravity is tested against the two established empirical relations for the SPARC catalog, viz., the Radial Acceleration Relation (RAR) and the Baryonic Tully Fisher relation (BTFR), both are found to be satisfied consistently.