Abstract

The growth rate of geodesic deviation in a homogeneous and isotropic on average cosmological model, in which curvature fluctuations are taken into account, is studied. Using numerical simulation methods, it is shown that the growth rate of geodesic deviation increases with the increase in distance to the celestial body on a geodesic at the same rate as the length of the two-dimensional vector, composed of geodesic deviation and its derivative whose growth rate can be theoretically calculated in the so-called Furstenberg theory.

中文翻译：

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随机曲率雅可比方程中的Lyapunov指数和测地偏差增长率

摘要

研究了考虑曲率涨落的均匀各向同性平均宇宙学模型中测地偏差的增长率。利用数值模拟方法表明，测地偏差的增长率随着测地线上距天体距离的增加而增加，其增长率与二维矢量的长度相同，该二维矢量由测地偏差及其导数组成，其增长率可以用所谓的弗斯滕伯格理论进行理论上计算。