标题： 爱因斯坦引力的一般模型与非牛顿弱场极限 显示英文标题

标题： General models of Einstein gravity with a non-Newtonian weak-field limit

摘要： 我们研究了与标量场\vphi 和点状物质耦合的爱因斯坦引力理论，这些理论由依赖于标量场的物质耦合函数 e^{H(\vphi )}特征化。 我们表明，在对标量场势能形式施加适度约束的情况下，存在一大类爱因斯坦类似引力模型——其特征是 H 的渐近行为——允许非牛顿的弱场极限，其中引力势在大距离处的行为为 ln r。牛顿项 GM/r 仅作为次级项出现。 我们指出，这种行为也存在于由 f(R) 拉格朗日量描述的引力模型中。 我们的结果对于构建红外修改的引力理论以及修改牛顿动力学的相关性也进行了讨论。 显示英文摘要

摘要： We investigate Einstein theories of gravity, coupled to a scalar field \vphi and point-like matter, which are characterized by a scalar field-dependent matter coupling function e^{H(\vphi)}. We show that under mild constraints on the form of the potential for the scalar field, there are a broad class of Einstein-like gravity models -characterized by the asymptotic behavior of H- which allow for a non-Newtonian weak-field limit with the gravitational potential behaving for large distances as ln r. The Newtonian term GM/r appears only as sub-leading. We point out that this behavior is also shared by gravity models described by f(R) Lagrangians. The relevance of our results for the building of infrared modified theories of gravity and for modified Newtonian dynamics is also discussed.