Exploring non-minimal coupling using ultra-diffuse galaxies

Abstract

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: 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. We further validate the analysis through a sensitivity test on mock Dragonfly 44 data, which shows that only large couplings, which are already disfavored by the data, produce a detectable imprint, while smaller values remain indistinguishable from General Relativity at the current observational precision. 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. These upper limits should be interpreted as a sensitivity limit of current UDG kinematics rather than as a tight exclusion of the coupling. Future high precision velocity measurements will be essential to determine whether non-minimal coupling effects can become observationally distinguishable in low-acceleration systems.