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We review the distance modulus in twelve different cosmologies: the$\Lambda$CDM model, the wCDM model, the Cardassian model, the flat case, the$\phi$CDM cosmology, the Einstein--De Sitter model, the modified Einstein--DeSitter model, the simple~GR model, the flat expanding model, the Milne model,the plasma model and the modified tired light model. The above distance moduliare processed for three different compilations of supernovae and a supernovae +GRBs compilation: Union 2.1, JLA, the Pantheon and Union 2.1 + 59 GRBs. Foreach of the 48 analysed cases we report the relative cosmological parameters,the chi-square, the reduced chi-square, the AIC and the $Q$ parameter. Theangular distance as function of the redshift for five cosmologies is reportedin the framework of the minimax approximation.

Sparse formulae for the distance modulus in cosmology