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 μ(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 μ that varies too gradually, and it fits rotation curves less well than the standard MOND interpolating function μ(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.
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机译：Bekenstein认为通常用暗物质或修正的牛顿动力学（MOND）来描述的现象是协变标量场的结果，该协变标量场由自由函数[与MOND内插函数μ（g / a_0）有关]控制拉格朗日密度。在这种相对论的MOND理论（TeVeS）的背景下，我们批判性地研究了弱重力和强重力之间过渡区域中的插值函数。 Bekenstein的玩具模型产生的μ的变化太大，并且其旋转曲线的拟合效果不如标准MOND插值函数μ（x）= x /（1 + x〜2）〜（1/2）。但是，后者变化太大，暗示了难以置信的外部场效应。相对两侧的这些约束尚未排除TeVeS，但它们使可接受的插值函数的区域变窄。具有简单分析特性的可接受的“玩具”拉格朗日密度函数被选出用于星系中的TeVeS的未来研究。我们还建议如何将模型扩展到太阳系动力学和宇宙学。
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