A first attempt to differentiate between modified gravity and modified inertia with galaxy rotation curves

The phenomenology of modified Newtonian dynamics (MOND) on galaxy scales may point to more fundamental theories of either modified gravity (MG) or modified inertia (MI). In this paper, we test the applicability of the global deep-MOND parameter Q which is predicted to vary at the 10% level between MG and MI theories. Using mock-observed analytical models of disk galaxies, we investigate several observational uncertainties, establish a set of quality requirements for actual galaxies, and derive systematic corrections in the determination of Q. Implementing our quality requirements to the SPARC database yields 15 galaxies, which are close enough to the deep-MOND regime as well as having rotation curves that are sufficiently extended and sampled. For these galaxies, the average and median values of Q seem to favor MG theories, albeit both MG and MI predictions are in agreement with the data within 1.5 sigma. Improved precision in the determination of Q can be obtained by measuring extended and finely-sampled rotation curves for a significant sample of extremely low-surface-brightness galaxies.