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

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.