Dark matter, modified gravity, and the mass of the neutrino

It has been suggested that Einstein's theory of general relativity can be modified to accommodate mismatches between the gravitational field and luminous matter on a wide range of scales. Covariant theories of modified gravity generically predict the existence of extra degrees of freedom which may be interpreted as dark matter. We study a subclass of these theories where the overall energy density in these extra degrees of freedom is subdominant relative to the baryon density. We find that, although all theories we consider favor the presence of massive neutrinos, it is generally not possible to establish a lower limit on the neutrino mass. For a few very specific cases (such as a flat universe with a cosmological constant), we find a conservative lower bound on the neutrinos mass of m_>0. 31 eV.