Exploring Non-minimal coupling using ultra-diffuse galaxies

We investigate whether a non-minimal coupling between dark matter and gravity can influence the internal dynamics of ultra-diffuse galaxies. Within this framework, the gravitational potential is modified by an additional term that captures the interaction between spacetime curvature and the dark matter with a coupling constant determined by a length scale $L$. Using spherical Jeans modeling, we analyze the kinematic data of three ultra-diffuse galaxies namely: NGC\;1052-DF2, NGC\;1052-DF4, and Dragonfly\;44, which span the observational extremes from dark matter deficient to dark matter dominated systems. For each galaxy we explore several dark matter halo profiles, two orbital anisotropy models, and both with and without Stellar-to-Halo Mass Relation scenarios, and we perform a Bayesian parameter inference. Our results show that across all the considered configurations, the constrained astrophysical parameters are consistent with standard ones from General Relativity. The posterior distributions of $L$ show no preference for non-zero values and result only in upper limits, suggesting that any non-minimal coupling contribution must be small and perturbative on this scales. Future high precision velocity measurements will be essential to determine whether non-minimal coupling effects can become observationally distinguishable in low-acceleration systems.