Finite-Scale Theory of Gravity in Galaxy Dynamics: A Comparative Analysis of Spiral and Early- Type Galaxies

We present a systematic comparison of the Finite-Scale Theory (FST) of gravity against established models—baryonic-only, Modified Newtonian Dynamics (MOND), and Navarro-Frenk-White (NFW) dark matter—using two complementary galaxy samples: 175 spiral galaxies from the SPARC database (rotation curves) and 73 early-type galaxies with independently measured distances from the ATLAS3D survey (velocity dispersion profiles). Model comparison is performed via the Bayesian Information Criterion (BIC). For SPARC spirals, FST achieves a 46.3% win rate (81/175), significantly outperforming MOND (26.3%) and LCDM (27.4%), with 18.3% of galaxies showing strong statistical preference (ΔBIC > 2). For the 73 ATLAS3D early-type galaxies with real parameters, NFW is the best model in 89% of galaxies (65/73), while FST wins in only 11% (8/73). However, a critical velocity-scale parameter v₀ emerges as a decisive discriminator: among the 6 galaxies with v₀ > 150 km s⁻¹, FST wins ~67% (4/6). This is consistent with SPARC results where v₀ > 150 km s⁻¹ yields ~80% FST win rate, but the small sample size (6 galaxies, 8.2% of the 73-galaxy sample) means this should be interpreted as a qualitative trend requiring confirmation rather than a statistically robust result.