Refining the MOND interpolating function and TeVeS Lagrangian

The phenomena customarily described with dark matter or modified Newtonian dynamics (MOND) have been argued by Bekenstein to be the consequences of a covariant scalar field, controlled by a free function [related to the MOND interpolating function mu(g/a(0))] in its Lagrangian density. In the context of this relativistic MOND theory (TeVeS), we examine critically the interpolating function in the transition zone between weak and strong gravity. Bekenstein's toy model produces a mu that varies too gradually, and it fits rotation curves less well than the standard MOND interpolating function mu(x) = x/(1 + x(2))(1/2). However, the latter varies too sharply and implies an implausible external field effect. These constraints on opposite sides have not yet excluded TeVeS, but they have made the zone of acceptable interpolating functions narrower. An acceptable toy Lagrangian density function with simple analytical properties is singled out for future studies of TeVeS in galaxies. We also suggest how to extend the model to solar system dynamics and cosmology.