Discrete Newtonian Cosmology

TL;DR

This paper develops a Newtonian framework for cosmology at scales smaller than the Hubble radius, deriving standard cosmological equations from particle interactions without continuum assumptions or general relativity.

Contribution

It introduces a purely Newtonian cosmological model based on point particles, deriving the Friedmann and Raychaudhuri equations without fluid or continuum approximations.

Findings

Exact solutions for homothetic particle expansion

Validation of standard cosmological equations in Newtonian context

Framework applicable to dark matter, galaxies, and clusters

Abstract

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.