Analytical Approach for the Determination of the Luminosity Distance in a Flat Universe with Dark Energy

TL;DR

This paper derives an efficient approximate analytical formula for calculating luminosity distance in a flat, dark energy dominated universe, reducing computational effort compared to traditional numerical methods.

Contribution

It introduces a novel, highly accurate analytical expression for luminosity distance in flat universe models with dark energy, streamlining calculations.

Findings

The analytical formula has very small uncertainties.

It significantly improves computational efficiency.

Applicable for Monte-Carlo simulations involving luminosity distances.

Abstract

Recent cosmological observations indicate that the present universe is flat and dark energy dominated. In such a universe, the calculation of the luminosity distance, d_L, involve repeated numerical calculations. In this paper, it is shown that a quite efficient approximate analytical expression, having very small uncertainties, can be obtained for d_L. The analytical calculation is shown to be exceedingly efficient, as compared to the traditional numerical methods and is potentially useful for Monte-Carlo simulations involving luminosity distances.