An analytical approximation of the luminosity distance in flat cosmologies with dark energy

TL;DR

This paper introduces an analytical approximation for the luminosity distance in flat cosmologies with dark energy, providing accurate and useful formulas for gravitational lensing analysis across a broad range of parameters.

Contribution

The authors develop a new analytical approximation for luminosity and Dyer-Roeder distances in flat cosmologies with dark energy, improving accuracy over previous models.

Findings

Relative error less than previous models within specified parameter ranges.

Applicable for redshift range 0.03 to 1000 and density parameter 0.3 to 1.

Useful for gravitational lensing analysis in cosmology.

Abstract

We present an analytical approximation formula for the luminosity distance in spatially flat cosmologies with dust and a cosmological constant. We also show the approximate formulae for the so-called Dyer-Roeder distance (empty beam case) and the generalised angular diameter distance from redshift $z=z_1$ to $z=z_2$, which are particularly useful in analysing the gravitational lens effects. Our formulae are widely applicable over the range of the density parameter and the redshift with sufficiently small uncertainties. In particular, in the range of density parameter $0.3 \lid \Omega_{\rmn m} \lid 1$ and redshift $0.03 \lid z \lid 1000$, the relative error for the luminosity distance by our formula is always smaller than that of the recent work by \cite{wu}.