A Series Solution to the Luminosity Distance in a Flat LCDM Universe

TL;DR

This paper derives a series solution for the luminosity distance in a flat LCDM universe, significantly reducing computational complexity while maintaining high accuracy across a range of parameters and redshifts.

Contribution

It introduces a novel series solution for luminosity distance in flat LCDM cosmology, improving computational efficiency and accuracy over traditional numerical methods.

Findings

Relative error less than 0.36% for a wide parameter range

Series converges rapidly with order n=100

Applicable for redshift z > 0.1

Abstract

Cosmological observations indicate that our universe is flat and dark energy (DE) dominated at present. The luminosity distance plays an important role in the investigation of the evolution and structure of the universe. Nevertheless, the evaluation of the luminosity distance d_L is associated computationally heavy numerical quadratures in practice. In this Letter we find a series solution of the luminosity distance in a spatially flat LCDM cosmological model. And it is further shown that the series solution has a relative error of less than 0.36% for any relative parameter \beta (\beta = Omega_m / Omega_L) from zero to four, i.e. 0.2 < Omega_L < 1 and redshift z > 0.1 when the order of the series is n = 100.