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Planck Collaboration (2018) Planck 2018 Results. VI. Cosmological Parameters. arXiv:1807.06209. (Preprint)

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• TITLE: Sparse Formulae for the Distance Modulus in Cosmology

  AUTHORS: Lorenzo Zaninetti

  KEYWORDS: Cosmology, Observational Cosmology, Distances, Redshifts, Radial Velocities, Spatial Distribution of Galaxies, Magnitudes and Colours, Luminosities

  JOURNAL NAME: Journal of High Energy Physics, Gravitation and Cosmology, Vol.7 No.3, July 6, 2021

  ABSTRACT: We review the distance modulus in twelve different cosmologies: the ΛCDM model, the wCDM model, the Cardassian model, the flat case, the ?CDM cosmology, the Einstein—De Sitter model, the modified Einstein—De Sitter model, the simple GR model, the flat expanding model, the Milne model, the plasma model and the modified tired light model. The above distance moduli are processed for three different compilations of supernovae and a supernovae + GRBs compilation: Union 2.1, JLA, the Pantheon and Union 2.1 + 59 GRBs. For each of the 48 analysed cases we report the relative cosmological parameters, the chi-square, the reduced chi-square, the AIC and the Q parameter. The angular distance as function of the redshift for five cosmologies is reported in the framework of the minimax approximation.