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Galaxies 2016, 4(1), 4; doi:10.3390/galaxies4010004

Padé Approximant and Minimax Rational Approximation in Standard Cosmology

Dipartimento di Fisica, Università degli Studi di Torino, via P.Giuria 1, I-10125 Turin, Italy
Academic Editor: Emilio Elizalde
Received: 12 November 2015 / Revised: 21 January 2016 / Accepted: 21 January 2016 / Published: 18 February 2016
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Abstract

The luminosity distance in the standard cosmology as given by ΛCDM and, consequently, the distance modulus for supernovae can be defined by the Padé approximant. A comparison with a known analytical solution shows that the Padé approximant for the luminosity distance has an error of 4 % at redshift = 10 . A similar procedure for the Taylor expansion of the luminosity distance gives an error of 4 % at redshift = 0 . 7 ; this means that for the luminosity distance, the Padé approximation is superior to the Taylor series. The availability of an analytical expression for the distance modulus allows applying the Levenberg–Marquardt method to derive the fundamental parameters from the available compilations for supernovae. A new luminosity function for galaxies derived from the truncated gamma probability density function models the observed luminosity function for galaxies when the observed range in absolute magnitude is modeled by the Padé approximant. A comparison of ΛCDM with other cosmologies is done adopting a statistical point of view. View Full-Text
Keywords: cosmology; observational cosmology; distances; redshifts; radial velocities; spatial distribution of galaxies; magnitudes and colors; luminosities cosmology; observational cosmology; distances; redshifts; radial velocities; spatial distribution of galaxies; magnitudes and colors; luminosities
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Zaninetti, L. Padé Approximant and Minimax Rational Approximation in Standard Cosmology. Galaxies 2016, 4, 4.

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