For modified gravity, it's the LITTLE THINGS that matter

Dwarf galaxies have long been recognised as important testing grounds for models of dark matter. For instance, it is here where the cusp-core problem is most apparent. In this work we select two dwarf galaxy samples: LITTLE THINGS and dwarf galaxies in SPARC. We use these to examine whether there are preferences for MOND or dark matter halos in these objects. Notably, our analysis employs the latest developments in Hamiltonian Monte Carlo sampling methodology and robust model comparison via ELPD differences. Our findings suggest a $>4\sigma$ preference for cored halo models over MOND. However, this relies on significant preferences from 7 out of 19 SPARC galaxies and 11 of 18 from LITTLE THINGS (few of which are overwhelming). It is notable that only a single galaxy prefers MOND over a cored halo. Thus, this evidence is suggestive, but does not conclusively decide against MOND. We also test for evidence of a MOND external field effect, and find weak evidence against its presence. Despite these statistical preferences, most SPARC galaxies remain compatible with a universal MOND scale. In LITTLE THINGS, a free MOND model is preferred to a universal value at $\sim 8\sigma$, but this is of doubtful physical significance. For MOG, the story is different, here we find $\gtrsim 8\sigma$ preferences for all halos (or MOND) against universal MOG models with significant exclusions in individual galaxies across both samples. Thus, a proposed universal rotation curve model derived from MOG is quite strongly disfavoured.