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The random-motion theorem in a local cosmology with dark energy
Authors:A D Chernin  VP Dolgachev  LM Domozhilova  P Teerikorpi  M Yu Valtonen
Institution:(1) CERCA, Department of Physics, Case Western Reserve University, 10900 Euclid Ave, Cleveland, OH 44106-7079, USA
Abstract:It is shown that the random-motion theorem in cosmology proven in the early 1960s can be generalized to take into account the presence of a uniform dark-energy background. The role of the dark energy is substantial: its repulsive force exceeds the gravitational force due to darkmatter and baryons, both on the scale of the Universe as a whole and on local scales of about 1 Mpc. The generalized random-motion theorem has the form of a differential equation relating the kinetic energy of the random motion and the potential energy of the particles due to their own gravitational field and the repulsive dark-energy field. One consequence of the generalized theorem is a virial relation containing the potential energy in the repulsive field.
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