Discrete Newtonian Cosmology: Perturbations

TL;DR

This paper extends discrete Newtonian cosmology to include perturbations, deriving linearized structure growth equations and the Dmitriev-Zeldovich equations, revealing insights into voids with apparent negative mass.

Contribution

It demonstrates how to obtain perturbed solutions in discrete Newtonian cosmology that match general relativity's linear structure growth equations.

Findings

Perturbed solutions reproduce GR linear structure growth equations.

Derived Dmitriev-Zeldovich equations for subsystems.

Showed voids can have an apparent negative mass.

Abstract

In a previous paper [arXiv:1308.1852] we showed how a finite system of discrete particles interacting with each other via Newtonian gravitational attraction would lead to precisely the same dynamical equations for homothetic motion as in the case of the pressure-free Friedmann-Lema\^{i}tre-Robertson-Walker cosmological models of General Relativity Theory, provided the distribution of particles obeys the central configuration equation. In this paper we show one can obtain perturbed such Newtonian solutions that give the same linearised structure growth equations as in the general relativity case. We also obtain the Dmitriev-Zeldovich equations for subsystems in this discrete gravitational model, and show how it leads to the conclusion that voids have an apparent negative mass.