As it has been recently demonstrated, the mathematical model with the hyperbolic space (or, in other words, with the negative spatial curvature) is the most appropriate one for describing the inhomogeneous Universe at late stages of its evolution in the framework of the theory of scalar perturbations. In this model we develop a dynamic approach and investigate nonrelativistic motion of two, three and even more cosmic bodies against the cosmological background, perturbed locally by density inhomogeneities (namely, galaxies). For arbitrary initial conditions, we get solutions of equations of motion (trajectories), demonstrating the most important features of cosmological expansion, only slightly restrained by gravitational attraction. We use our methods for indirect observations of dark energy in the Local Group, analyzing the relative motion of the Milky Way and Andromeda galaxies. The numerical estimation of the time before their collision is obtained. Besides that we consider the Hubble flows anisotropy caused by the non-point mass distribution.
inhomogeneous Universe; Local Group; Hubble flows.
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