Cosmological implications of phase coupling gravity

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Abstract
Phase Coupling Gravitation (PCG) is a theory proposed by Bekenstein to account for observed astronomical mass discrepancies without evoking the presence of significant quantities of dark matter in the Universe. The theory involves the addition of a complex scalar field to the usual tensor field of General Relativity, but only the phase of the complex scalar couples to ordinary matter. Here the cosmological equations for the theory are written down and general constraints on the form of the self-interaction potential of the scalar field are derived. The requirement of a physically viable cosmology implies that, in the context of PCG, there exists a maximum conventional mass discrepancy associated with any mass concentration and a return to Newton's law on the largest scale. Detailed cosmological models are calculated for the special case of a linear potential which satisfies the general constraints and which, in an evolving universe, can predict the observed form of galaxy rotation curves. The resulting cosmological models resemble the usual Friedman models with an arbitrary cosmological constant which, as usual, can be tuned to obtain zero curvature with the observed density of visible matter. The essential observational prediction of the theory independent of the form of the self-interaction potential is time variability of the gravitational constant which is at least as large as one-tenth of the present experimental limit. In the specific models calculated, G is a few per cent larger at the epoch of nucleosynthesis than at the present, but this is offset by the low baryonic density (no baryonic dark matter); therefore the predicted fraction of primordial helium (23.3 per cent) is consistent with the abundance inferred from observations.

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