We look for empirical evidence of a nonminimal coupling (NMC) between dark matter (DM) and gravity in the
dynamics of local spiral galaxies. In particular, we consider a theoretically motivated NMC that may arise
dynamically from the collective behavior of the coarse-grained DM field (e.g., via Bose–Einstein condensation)
with averaging/coherence length L. In the Newtonian limit, this NMC amounts to modify the Poisson equation by
a term L2∇2ρ proportional to the Laplacian of the DM density itself. We show that such a term, when acting as a
perturbation over the standard Navarro–Frenk–White profile of cold DM particles, can substantially alter the
dynamical properties of galaxies, in terms of their total radial acceleration within the disk and rotation velocity.
Specifically, we find that this NMC model can properly fit the stacked rotation curves (RCs) of local spiral galaxies
with different velocities at the optical radius, including dwarfs and low-surface-brightness systems, at a level of
precision comparable to, and in some instances even better than, the phenomenological Burkert profile. Finally, we
show that by extrapolating down to smaller masses the scaling of L versus halo mass found from the above RC
analysis, the NMC model can adequately reproduce the radial acceleration relation in shape and normalization
down to the dwarf spheroidal galaxy range, a task which constitutes a serious challenge for alternative DM models
even inclusive of baryonic effects.
