Numerical Strategies of Computing the Luminosity Distance

Abstract

We propose two efficient numerical methods of evaluating the luminosity distance in the spatially flat ΛCDM universe. The first method is based on the Carlson symmetric form of elliptic integrals, which is highly accurate and can replace numerical quadratures. The second method, using a modified version of Hermite interpolation, is less accurate but involves only basic numerical operations and can be easily implemented. We compare our methods with other numerical approximation schemes and explore their respective features and limitations. Possible extensions of these methods to other cosmological models are also discussed.

4 pages, 2 figures. v2: A minor error in the last equation has been corrected (conclusions are not affected). v3: Accepted by MNRAS

References in corpus (4)

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• Brief Note: Analytical Fit to the Luminosity Distance for Flat Cosmologies with a Cosmological Constant
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• A new analytical solution for the distance modulus in flat cosmology
• A new analytical approximation of luminosity distance by optimal HPM-Padé technique
• Analytic auto-differentiable $\Lambda$CDM cosmography
• Degeneracy and Discreteness in Cosmological Model Fitting
• Computing the luminosity distance via optimal homotopy perturbation method
• Quadrature algorithms to the luminosity distance with a time-dependent dark energy model