Bridging the gap between dark matter and MOND by a relativistc scalar field approach

A Lagrangian model for a general relativistic scalar field, formulated in the framework of integrable Weyl geometry, is studied. Under the present assumptions it modifies the light cone structure and induces MOND-like dynamics in the weak field approximation of the Einstein frame (gauge). The Lagrangian contains a Bekenstein-type (“aquadratic”) term and a second order term generating additional mass energy for the scalar field. Both are switched on only if the scalar field gradient is spacelike and below a MOND-typical threshold, like in the superfluid model of Berezhiani/Khoury. In the weak field limit the Bekenstein term implies a deep MOND equation for the scalar field and leads to MONDian free fall trajectories. The Lagrangian mass term induces non-negligible energy and pressures of the scalar field with the respective consequences for gravitational light deflection.