An analytical approach for the determination of the luminosity distance in a flat universe with dark energy

Recent cosmological observations indicate that the present universe is flat and dark energy dominated. In such a universe, the calculation of the luminosity distance, d(L), involves repeated numerical calculations. In this paper, it is shown that a quite efficient approximate analytical expression, having very small uncertainties, can be obtained for d(L). The analytical calculation is shown to be exceedingly efficient, as compared to the traditional numerical methods, and is potentially useful for Monte Carlo simulations involving luminosity distances.