Newtonian self-gravitating system in a relativistic huge void universe model

TL;DR

This paper investigates how large-scale voids in a relativistic universe model affect the evolution of density perturbations, challenging the assumptions of the Copernican Principle and revealing significant differences from standard cosmological models.

Contribution

It develops a Newtonian approximation for perturbations in a huge void universe without assuming the Copernican Principle, deriving and solving equations that show distinct perturbation behaviors.

Findings

Perturbation equations differ significantly from homogeneous models.

Density perturbation behaviors are markedly different in void regions.

The approach accounts for anisotropic expansion effects.

Abstract

We consider a test of the Copernican Principle through observations of the large-scale structures, and for this purpose we study the self-gravitating system in a relativistic huge void universe model which does not invoke the Copernican Principle. If we focus on the the weakly self-gravitating and slowly evolving system whose spatial extent is much smaller than the scale of the cosmological horizon in the homogeneous and isotropic background universe model, the cosmological Newtonian approximation is available. Also in the huge void universe model, the same kind of approximation as the cosmological Newtonian approximation is available for the analysis of the perturbations contained in a region whose spatial size is much smaller than the scale of the huge void: the effects of the huge void are taken into account in a perturbative manner by using the Fermi-normal coordinates. By using this approximation, we derive the equations of motion for the weakly self-gravitating perturbations whose elements have relative velocities much smaller than the speed of light, and show the derived equations can be significantly different from those in the homogeneous and isotropic universe model, due to the anisotropic volume expansion in the huge void. We linearize the derived equations of motion and solve them. The solutions show that the behaviors of linear density perturbations are very different from those in the homogeneous and isotropic universe model.