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Analytical Approach for the Determination of the Luminosity Distance in a Flat Universe with Dark Energy
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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, involve 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.
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The distance modulus in dark energy and Cardassian cosmologies via the hypergeometric function
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