Numerical Strategies of Computing the Luminosity Distance

TL;DR

This paper introduces two efficient numerical methods for computing the luminosity distance in a flat DM universe, one highly accurate using elliptic integrals and another simpler with Hermite interpolation, comparing their features and potential extensions.

Contribution

The paper presents two novel numerical approaches for calculating luminosity distance, improving accuracy and simplicity over existing schemes in cosmology.

Findings

The elliptic integral method achieves high accuracy in luminosity distance calculations.

The Hermite interpolation method is computationally simple and easy to implement.

Both methods are compared favorably with existing approximation schemes.

Abstract

We propose two efficient numerical methods of evaluating the luminosity distance in the spatially flat {\Lambda}CDM universe. The first method is based on the Carlson symmetric form of elliptic integrals, which is highly accurate and can replace numerical quadratures. The second method, using a modified version of Hermite interpolation, is less accurate but involves only basic numerical operations and can be easily implemented. We compare our methods with other numerical approximation schemes and explore their respective features and limitations. Possible extensions of these methods to other cosmological models are also discussed.