Lyapunov exponent and the growth rate of geodesic deviation in the Jacobi equation with random curvature

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.