Alternatives to dark matter

The required matching of falling disc rotation curves with rising halo rotation curves in order to produce flat rotation curves in the outer parts of spiral galaxies covering a wide range in mass and size places strong constraints on dark matter hypotheses. This ‘disc–halo conspiracy’ is explained naturally by radical suggestions that the law of gravity is not the usual inverse square law in the limit of large distances from mass concentrations. The two recently suggested modifications of Newtonian gravity are considered in the light of general constraints on classical gravity theories and observations of mass discrepancies in galaxies and groups of galaxies. The relativistic theory of Bekenstein and Milgrom can satisfy most requirements on a gravity theory, but relativistic versions of finite length scale anti-gravity suggested by the present author are either inconsistent with geodesic motion of particles locally or contain a ghost field. Observational contradictions are apparent for both suggested hypotheses. A third theory, derived by a trivial modification of the Bekenstein–Milgrom Lagrangian, can account for the present observed systematics of mass discrepancies in the Universe and can predict from the observed distribution of visible matter the detailed rotation curves of several well-observed spiral galaxies ranging in size from 8 to 80 kpc.