Testing Covarying Coupling Constants (CCC) against the full SPARC rotation-curve sample: a like-for-like comparison with MOND and NFW

Abstract

The Covarying Coupling Constants (CCC) framework, developed to account for high-redshift JWST observations, contains a mechanism -- a covarying-constant effective mass field keyed to local density -- that modifies galactic dynamics without particle dark matter. We test it against the full Spitzer Photometry and Accurate Rotation Curves (SPARC) sample of 175 disc galaxies, extending an earlier study of a few objects. Working in an inverse formulation, in which each model predicts the baryonic rotation curve from the observed one, we compare CCC against Modified Newtonian Dynamics (MOND) and one- and two-parameter Navarro-Frenk-White (NFW) haloes on identical footing, using the reduced $\chi^2_\nu$. We show that the published sharp density turn-off in the earlier study is unphysical and replace it with a smooth transition -- the density-space analogue of the MOND interpolating function, introducing no new parameter. One-parameter smooth-CCC then performs comparably to galaxy-by-galaxy fitted MOND (the lower $\chi^2_\nu$ in 56 per cent of galaxies, mean $\chi^2_\nu$ of 2.58 versus 2.65; the paired difference is not significant), while two-parameter NFW shows a substantially broader fit-quality distribution and a larger tail of poor or boundary-limited fits (mean $\chi^2_\nu \approx 7$). The CCC turn-off density is not universal (scatter 0.82 dex) and correlates with galaxy size, qualitatively consistent with a spherical reconstruction applied to flattened disc systems. Recast as an acceleration, however, $a_t = V_{\rm flat}^2/R_t$ has scatter 0.33 dex (on the 91-galaxy resolved subset) -- matching the MOND scale $a_0$ (0.34 dex) -- and comparable magnitude of order $2 \times 10^{-10}$ m/s$^2$, with its size correlation removed. Though not designed for galactic dynamics, CCC describes rotation curves as well as galaxy-by-galaxy fitted MOND.