平坦FRW宇宙中的延迟宇宙引力和马赫原理
Retarded cosmological gravity and Mach's principle in flat FRW universes
摘要：
可观测宇宙的物质和能量含量所产生的延迟引力公式化，并显示这种宇宙引力如何引起加速参考系中的惯性力。该模型是为空间平坦的Friedman-Robertson-Walker（FRW）宇宙开发的。首先在基本参照系、Einstein-de Sitter（ES）模型和LambdaCDM模型中确定了宇宙引力的延迟势。在ES宇宙中，尽管膨胀，可观测宇宙仍产生一个静态的、滞后的引力势，其大小为c2，而在LambdaCDM模型中，引力在膨胀过程中减弱。在宇宙小区域的局部闵可夫斯基时空中，导出了在宇宙引力场中运动的试验体的协变拉格朗日量。惯性力由试验体的欧拉-拉格朗日方程以牛顿近似确定。模型计算表明，惯性力与ES宇宙中观测到的力完全吻合，马赫原理在ES宇宙中成立。在目前的标准中，LambdaCDM模型的惯性力比预期弱10%。
英文摘要：
The retarded gravitation produced by the matter and energy content of the observable universe is formulated and shown how this cosmological gravity gives rise to inertial forces in accelerated frames of reference. The model is developed for spatially flat Friedman-Robertson-Walker (FRW) universes. The retarded potential of cosmological gravity is determined first in fundamental frames of reference, in Einstein-de Sitter (ES)and in LambdaCDM models. Despite the expansion, the observable universe gives rise to a static, retarded gravitational potential equal to c2 in ES universe, while gravity is weakening during the expansion in LambdaCDM model. In the locally Minkowski spacetime occurring in a small domain of the universe, a covariant Lagrangian of a test body moving in the cosmological gravitational field is derived. Inertial forces are determined from a test body's Euler-Lagrange equation, in Newtonian approximation. The model calculation indicates, that the inertial forces meet exactly the ones observed in ES universe and Mach's principle holds there. In the present-day standard, LambdaCDM model inertial forces are weaker by 10 % than expected.
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