  A recent study by Farnes (2018) proposed an alternative cosmological model in
which both dark matter and dark energy are replaced with a single fluid of
negative mass. This paper presents a critical review of that model. A number of
problems and discrepancies with observations are identified. For instance, the
predicted shape and density of galactic dark matter halos are incorrect. Also,
halos would need to be less massive than the baryonic component otherwise they
would become gravitationally unstable. Perhaps the most challenging problem in
this theory is the presence of a large-scale version of the `runaway' effect,
which would result in all galaxies moving in random directions at nearly the
speed of light. Other more general issues regarding negative mass in general
relativity are discussed, such as the possibility of time-travel paradoxes.
