Sparse formulae for the distance modulus in cosmology

TL;DR

This paper reviews and compares the distance modulus calculations across twelve cosmological models using various supernovae and GRB data sets, providing detailed statistical analyses and approximations.

Contribution

It introduces a comprehensive comparison of distance moduli in multiple cosmologies with statistical evaluations and minimax approximations for angular distance functions.

Findings

Relative cosmological parameters are reported for each case.

Statistical measures like chi-square, AIC, and Q are provided.

Angular distance functions are approximated for five cosmologies.

Abstract

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--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.