A new analytical approximation of luminosity distance by optimal HPM-Pad\'e technique

TL;DR

This paper introduces a new analytical approximation for luminosity distance in a flat universe using the HPM-Padé technique, demonstrating improved accuracy over a range of redshifts and validating it with observational data.

Contribution

The paper presents a novel analytical approximation method for luminosity distance using HPM-Padé, enhancing accuracy and robustness compared to existing models.

Findings

The approximation significantly improves accuracy over traditional methods.

It fits observational data well, including supernovae and H(z) measurements.

The method is validated using MCMC data fitting.

Abstract

By the use of homotopy perturbation method-Pad\'e (HPM-Pad\'e) technique, a new analytical approximation of luminosity distance in the flat universe is proposed, which has the advantage of significant improvement for accuracy in approximating luminosity distance over cosmological redshift range within $0\leq z\leq 2.5$. Then we confront the analytical expression of luminosity distance that is obtained by our new approach with the observational data, for the purpose of checking whether it works well. In order to probe the robustness of the proposed method, we also confront it to supernova type Ia and recent data on the Hubble expansion rate $H(z)$. Markov Chain Monte Carlo (MCMC) code emcee is used in the data fitting. The result indicates that it works fairly well.