Entropy-Response Gravity: Multi-Scale Tests from Dwarf Galaxies to Cluster Mergers
David Margetts, Anthony Margetts
Abstract
We present seven additional empirical tests of Entropy-Response Gravity (ERG), extending the multi-scale validation programme of Paper I (DOI: 10.5281/zenodo.19077317). ERG is built on the acceleration law g = g_b + √(a₀ g_b) where a₀ = 1.2×10⁻¹⁰ m s⁻², formally equivalent to the AQUAl scalar-field framework of Bekenstein & Milgrom (1984) at galaxy scales, while additionally incorporating a thermodynamic entropy source term β·σ in cluster environments.The seven tests span: wide binary stars (Chae 2025/2026, consistent at 1.24σ); KiDS-1000 weak lensing across four stellar mass bins (residual range 0.034 dex across log M★ = 9–11.5); 31,404 ALFALFA HI-selected galaxies (BTFR normalisation residual +0.007 dex); 15 M31 dwarf spheroidals (r = 0.748, p = 0.001); DESI DR2 cosmological coincidence (a₀/[cH₀/2π] = 1.1418); ACCEPT radial entropy profiles (outer ICM r = +0.22, p = 7×10⁻³³); and four cluster merger systems including the Bullet Cluster.The first order-of-magnitude calibration of the entropy coupling constant is derived: β/α ~ 2.8×10⁻²² K (J m⁻³)⁻¹ from ACCEPT radial profiles. Cluster merger infall speeds are shown to be ~10× more probable in ERG than in ΛCDM due to the deeper ERG potential wells. All seven tests are consistent with ERG predictions. Together with Paper I, ERG now passes twelve independent observational tests from sub-kpc to Mpc scales with a single constant a₀ and zero free parameters per galaxy.