Dwarf Galaxies without Dark Matter: constraints on Modified Gravity

The discovery of $19$ dwarf galaxies without dark matter provides, counter-intuitively, strong support for the $\Lambda$CDM standard model of cosmology. Their presence is well accommodated in a scenario where the dark matter is in the form of cold dark particles. However, it is interesting to explore quantitatively what is needed from modified gravity models to accommodate the presence of these galaxies and what extra degree of freedom is needed in these models. To this end, we derive the dynamics at galaxy scales (Virial theorem) for a general class of modified gravity models. We distinguish between theories that satisfy the Jebsen-Birkhoff theorem, and those that don't. Our aim is to develop tests that can distinguish whether dark matter is part of the theory of gravity or a particle. The 19 dwarf galaxies discovered provide us with a stringent test for models of modified gravity. Our main finding is that there will always be an extra contribution to the Virial theorem coming from the modification of gravity, even if a certain galaxy shows very small, if not negligible, trace of dark matter, as has been reported recently. Thus, if these and more galaxies are confirmed as devoid (or negligible) of dark matter, while other similar galaxies have abundant dark matter, it seems interesting to find modifications of gravity to describe dark matter. Our result can be used by future astronomical surveys to put constraints on the parameters of modified gravity models at astrophysical scales where dark matter is described as such.