Quadrature algorithms to the luminosity distance with a time-dependent dark energy model

TL;DR

This paper introduces and compares two quadrature algorithms, Romberg and Gaussian, for calculating luminosity distances in dark energy models, specifically focusing on the CPL parametrization, and proposes an efficient approximation strategy for flat LCDM universes.

Contribution

The paper presents two effective quadrature algorithms for luminosity distance calculations in dark energy models and introduces a new approximation strategy for flat LCDM universes.

Findings

Gaussian quadrature is more promising than Romberg integration.

The methods improve efficiency and accuracy in dark energy cosmology calculations.

Proposed strategies aid numerical simulations in dark energy research.

Abstract

In our previous work, we have proposed two methods for computing the luminosity distance d_{L}^{\Lambda} in LCDM model. In this paper, two effective quadrature algorithms, known as Romberg Integration and composite Gaussian Quadrature, are presented to calculate the luminosity distance d_{L}^{CPL} in the Chevallier-Polarski-Linder parametrization(CPL) model. By comparing the efficiency and accuracy of the two algorithms, we find that the second is more promising. Moreover, we develop another strategy adapted for approximating d_{L}^{\Lambda} in flat LCDM universe. To some extent, our methods can make contributions to the recent numerical stimulation for the investigation of dark energy cosmology.