Calculating luminosity distance versus redshift in FLRW cosmology via homotopy perturbation method

Abstract

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