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

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