2013/08/19 by Gary W Gibbons, George F R Ellis
Physics and Astronomy · #Cosmological principle #Cosmology #Cosmology and Gravitation Theories #Dark energy #Einstein #Friedmann equations #General relativity #Newtonian dynamics #Newtonian fluid #Point particle #Quantum Electrodynamics and Casimir Effect #Relativity and Gravitational Theory #Scale factor (cosmology) #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/31/2/025003
published as Classical and Quantum Gravity 31 (2), 025003 (2014) · 33 pages; typos fixed, references added, some clarifications
arxiv created 2013/08/19 · openalex publication_date 2013/11/27 · openalex created_date 2016/06/24 · arxiv updated 2017/04/05 · openalex updated_date 2026/08/05
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 our 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.