一类几何西格玛模型中的引力加速度
Gravitational acceleration in a class of geometric sigma models
摘要：
在这项工作中，我检查球对称解决方案的几何西格玛模型与四个标量场。这类模型原来是更广泛的标量-矢量-张量引力理论的一个子类。本研究的目的是探讨如何额外的四个自由度修改牛顿引力加速度。我把我的考虑限制在德西特背景中的点状源上。由此产生的引力加速度具有幂级数的形式，其中有四个主要项。第一个和第二个是熟悉的牛顿和MOND项，在短距离内占主导地位。第三项在远距离上占主导地位。它是负责宇宙加速膨胀的$Λ$ CDM项。最后，第四项提供了一个额外的排斥加速度，该加速度随距离呈指数增长。这个术语只有在超出可观测宇宙的极大距离才变得重要。至于计算的引力加速度的时间依赖性，它原来是非平凡的，振荡的字符。
英文摘要：
In this work, I examine spherically symmetric solutions in geometric sigma models with four scalar fields. This class of models turns out to be a subclass of the wider class of scalar-vector-tensor theories of gravity. The purpose of the present study is to examine how the additional four degrees of freedom modify Newtonian gravitational acceleration. I have restricted my considerations to pointlike sources in de Sitter background. The resulting gravitational acceleration has the form of a power series, with four major terms standing out. The first and the second are the familiar Newtonian and MOND terms, which dominate at short distances. The third term is dominant at large distances. It is the $Λ$CDM term responsible for the accelerated expansion of the Universe. Finally, the fourth term provides an extra repulsive acceleration that grows exponentially fast with distance. This term becomes significant only at extremely large distances that go beyond the observable Universe. As for the time dependence of the calculated gravitational acceleration, it turns out to have nontrivial, oscillatory character.
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