EFT Gravitational Enhancement: Empirical Test Against the Full SPARC Galaxy Sample

We test the gravitational enhancement function G_eff = 1/sqrt(mu(g_bar/a0)) derived from Entropic Field Theory (EFT) against the complete SPARC galaxy sample of 175 disk galaxies (Lelli, McGaugh & Schombert 2016, AJ 152, 157) and the Baryonic Tully-Fisher Relation (BTFR) dataset of Lelli, McGaugh & Schombert (2016, ApJL 816, L14). The EFT prediction uses zero free parameters: the stellar mass-to-light ratio is fixed at ML = 0.5 M_sun/L_sun and the acceleration scale a0 = 1.2 x 10^-10 m/s^2 is derived from the cosmological constant alone via a0 = (7/3) f_vac c^2 sqrt(Lambda/3).

Against the Radial Acceleration Relation (RAR), EFT achieves scatter of 0.174 dex, competitive with MOND-simple (0.170 dex) and MOND-standard (0.168 dex), while achieving the highest individual galaxy win rate at 65/135 (48%) compared to 37/135 (27%) for MOND-simple when ML is optimised per galaxy. Against the BTFR, EFT predicts a slope of exactly 0.25 (observed: 0.2552, bootstrap uncertainty ~0.004) and scatter of 0.060 dex in log(Vf), at or near the noise floor set by galaxy formation physics. Testing five velocity definitions against the Lelli et al. (2019, MNRAS 484, 3267) sample, Vf and Wp20/2 are the best tracers of EFT's asymptotic prediction, essentially tied at 0.063–0.064 dex, with inner velocities showing approximately twice this scatter. The a0 intercept is offset by +0.031 dex in log(Vf), corresponding to a factor 1.33 in a0, discussed in the context of ML systematics and the incompletely derived matter-coupling factor f_vac.

All data are taken directly from published machine-readable tables and verified field-by-field against published values. The theoretical basis for G_eff is developed in the companion paper (Adis 2026, EQ(vT), DOI: 10.5281/zenodo.15005630).