Discrete Newtonian Cosmology
  In this paper we lay down the foundations for a purely Newtonian theory of
cosmology, valid at scales small compared with the Hubble radius, using only
Newtonian point particles acted on by gravity and a possible cosmological term.
We describe the cosmological background which is given by an exact solution of
the equations of motion in which the particles expand homothetically with their
comoving positions constituting a central configuration. We point out, using
previous work, that an important class of central configurations are
homogeneous and isotropic, thus justifying the usual assumptions of elementary
treatments. The scale factor is shown to satisfy the standard Raychaudhuri and
Friedmann equations without making any fluid dynamic or continuum
approximations. Since we make no commitment as to the identity of the point
particles, our results are valid for cold dark matter, galaxies, or clusters of
galaxies. In future publications we plan to discuss perturbations of our
cosmological background from the point particle viewpoint laid down in this
paper and show consistency with much standard theory usually obtained by more
complicated and conceptually less clear continuum methods. Apart from its
potential use in large scale structure studies, we believe that out approach
has great pedagogic advantages over existing elementary treatments of the
expanding universe, since it requires no use of general relativity or continuum
mechanics but concentrates on the basic physics: Newton's laws for
gravitationally interacting particles.
