Sparse formulae for the distance modulus in cosmology

Abstract

We review the distance modulus in twelve different cosmologies: the $\Lambda$CDM model, the wCDM model, the Cardassian model, the flat case, the $\varphi$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.

24 pages and 11 figures. arXiv admin note: text overlap with arXiv:1602.06418

References in corpus (3)

• Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM
• Constraints on reconstructed dark energy model from SN Ia and BAO/CMB observations
• A new analytical solution for the distance modulus in flat cosmology