Computing the luminosity distance via optimal homotopy perturbation method

TL;DR

This paper introduces a new algorithm using an optimized homotopy perturbation method to accurately and efficiently compute luminosity distances in a flat universe with a cosmological constant.

Contribution

It presents an improved homotopy perturbation approach with optimization to enhance accuracy and robustness in calculating luminosity distances, addressing initial value arbitrariness.

Findings

The algorithm outperforms existing methods in accuracy.

It demonstrates higher computational efficiency.

The method shows robustness for different matter density parameters.

Abstract

We propose a new algorithm for computing the luminosity distance in the flat universe with a cosmological constant based on Shchigolev's homotopy perturbation method, where the optimization idea is applied to prevent the arbitrariness of initial value choice in Shchigolev's homotopy. Compared with the some existing numerical methods, the result of numerical simulation shows that our algorithm is a very promising and powerful technique for computing the luminosity distance, which has obvious advantages in computational accuracy,computing efficiency and robustness for a given {\Omega_m}.