An Approximate Analytical Algorithm for Evaluating the Distances in a Dark Energy Dominated Universe

TL;DR

This paper presents an approximate analytical method to calculate luminosity distances in a flat, vacuum-dominated universe, achieving high accuracy and computational efficiency compared to numerical approaches.

Contribution

It introduces a novel approximate analytical algorithm for evaluating cosmological distances in dark energy dominated universes, reducing computational complexity.

Findings

Achieves less than 0.02% error up to redshift 5

Provides a highly efficient alternative to numerical methods

Applicable for any vacuum energy value

Abstract

The most recent cosmological observations indicate that the present universe is flat and vacuum dominated. In such a universe, the distance measurements are always difficult and involve numerical computations. In this paper, it is shown that the most fundamental distance measurement of cosmology, the luminosity distance, for such a universe can be obtained in an approximate analytical way with very small errors of less than 0.02% up to %z = 5$ for any value of vacuum energy. The analytical calculation is shown to be exceedingly efficient, as compared to the traditional numerical methods.