Calculating Luminosity Distance versus Redshift in FLRW Cosmology via Homotopy Perturbation Method

TL;DR

This paper introduces an efficient analytical approach using the homotopy perturbation method to estimate luminosity distance in FLRW cosmology, replacing integral calculations with differential equation solutions for improved accuracy and simplicity.

Contribution

The paper presents a novel application of the homotopy perturbation method to derive analytical expressions for luminosity distance in FLRW models, enhancing computational efficiency.

Findings

Accurate analytical expressions for luminosity distance as a function of redshift.

Method simplifies calculations by solving differential equations instead of integrals.

Potential for extending the approach to other cosmological models.

Abstract

We propose an efficient analytical method for estimating the luminosity distance in a homogenous Friedmann-Lema\^itre-Robertson-Walker (FLRW) model of the Universe. This method is based on the homotopy perturbation method (HPM), which has high accuracy in many nonlinear problems, and can be easily implemented. For analytical calculation of the luminosity distance, we offer to proceed not from the computation of the integral, which determines it, but from the solution of a certain differential equation with corresponding initial conditions. Solving this equation by means of HPM, we obtain the approximate analytical expressions for the luminosity distance as a function of redshift for two different types of homotopy. Possible extension of this method to other cosmological models is also discussed.