Friedmann Limit of a point mass universe (is not Friedmann):Gravinational Lens Effect

TL;DR

This paper investigates the distance-redshift relation in a universe modeled with point particles, analyzing the effects of gravitational lensing and the universe's appearance as the number of particles becomes very large, while maintaining constant density.

Contribution

It provides a novel analysis of the gravitational lensing effects and the universe's appearance in a point particle model, clarifying the statistical amplification independent of particle number.

Findings

The statistical nature of lensing amplification is independent of the number of particles N.

The universe's appearance in the large N limit differs from the classical Friedmann model.

The analysis clarifies how point particle universes behave under gravitational lensing effects.

Abstract

We study the distance-redshift relation in a universe filled with point particles, and discuss what the universe looks like when we make the number of particles N very large, while fixing the averaged mass density. Using the Raychaudhuri equation and a simple analysis of the probability of strong lensing effects, we show that the statistical nature of the amplification is independent of N, and clarify the appearance of the point particle universe.