This book derives and analyzes all solutions to the Kepler problem with dark energy (DE), presenting significant results such as: (a) all radial infinite motions obey Hubble's law at large times; (b) all orbital infinite motions are asymptotically radial and obey Hubble's law; (c) infinite orbital motions strongly dominate the finite ones. This clearly shows the effect of repulsive DE: In the classical Kepler problem, all orbital motions are finite for negative energies and infinite in the opposite case. Another DE effect is spatial localization of bounded orbits: mostly, they are within the equilibrium sphere, where the attractive Newtonian force outbalances the repulsive force of DE.

This problem is of particular current interest due to recent studies of the local flows of galaxies showing domination of DE in their dynamics; the book discusses this observation in detail.

Presents a comprehensive analysis of all Kepler motions in the presence of dark energy Discusses in detail recent research on the role of dark energy in the local galactic flow dynamics Provides a detailed, clear, and consistent exposition of the topic

Autorentext

A.S. Silbergleit is an expert in mathematical and theoretical physics and author of over 160 papers and three books. His official biography can be found in "Who's Who In America". A.D. Chernin's work focuses on theoretical physics and cosmology. He is a professor at Moscow State University's Sternberg Astronomical Institute and has authored over 275 papers and about a dozen books.

Inhalt
Introduction.- Two-Body Problem with Dark Energy.- Radial Motions: Exact Solution and Its Analysis.- Orbital (Planar) Motions: Exact Solution and Its Analysis.- All Motions: Summary. Locality and Stability of Finite Motions.- Dark Energy and the Local Cosmic Flow.- Concluding Remarks.