A Simple Analytic Approximation of Luminosity Distance in FLRW Cosmology using Daftardar-Jafari Method

In this paper, the iterative method suggested by Daftardar-Gejji and Jafari hereafter called Daftardar-Jafari method (DJM) is applied for the approximate analytical representation of the luminosity distance in a homogenous Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology. We obtain the analytical expressions of the luminosity distance using the approximate solutions of the differential equation to which the luminosity distance satisfies, subject to the corresponding initial conditions. With the help of this approximate solution, a simple analytic formula for the luminosity distance as a function of redshift is obtained and compared with a numerical solution for the general integral formula by the Maple software. Subsequent comparison of the obtained approximate analytical formula with the corresponding numerical solution for the and quintessential models is provided and showed a high accuracy of the DJM approximations, at least for the certain values of parameters of the models. This comparison demonstrates the efficiency and simplicity of this approach to the problem of calculating the luminosity distance in theoretical cosmology.