Discrete matter, far fields, and dark matter

¹  Department of Mathematics, University of Milano - Via Saldini 50, I-20133 Milano, Italy, EU
²  Department of Physical and Mathematical Sciences, Insubria University Via Valleggio 11, I-22100 Como, Italy, EU

Corresponding author: carati@mat.unimi.it

Received: 24 April 2008
Accepted: 21 July 2008

Abstract

We show that in cosmology the gravitational action of the far away matter has quite relevant effects, if retardation of the forces and discreteness of matter (with its spatial correlation) are taken into account. The expansion rate is found to be determined by the density of the far away matter, i.e., by the density of matter at remote times. This leads to the introduction of an effective density, which has to be five times larger than the present one, if the present expansion rate is to be accounted for. The force per unit mass on a test particle is found to be of the order of 0.2 cH₀. The corresponding contribution to the virial of the forces for a cluster of galaxies is also discussed, and it is shown that it fits the observations if a decorrelation property of the forces at two separated points is assumed. So it appears that the gravitational effects of the far away matter may have the same order of magnitude as the corresponding local effects of dark matter.