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.
