The distance modulus in dark energy and Cardassian cosmologies via the hypergeometric function

TL;DR

This paper derives analytical solutions for the Hubble radius in dark energy and Cardassian cosmologies using hypergeometric functions, and applies these to supernova data to estimate cosmological parameters.

Contribution

It provides new analytical solutions for the Hubble radius in various cosmological models using hypergeometric functions, including approximate expansions.

Findings

Analytical solutions for Hubble radius in dark energy and Cardassian models.

Approximate Taylor expansions for equations of state.

Application to supernova data for parameter estimation.

Abstract

The presence of the dark energy allows both the acceleration and the expansion of the universe. In the case of a constant equation of state for dark energy we derived an analytical solution for the Hubble radius in terms of the hypergeometric function. An approximate Taylor expansion of order seven is derived for both the constant and the variable equation of state for dark energy. In the case of the Cardassian cosmology we also derived an analytical solution for the Hubble radius in terms of the hypergeometric function. The astronomical samples of the distance modulus for Supernova (SN) of type Ia allows the derivation of the involved cosmological in the case of constant equation of state, variable equation of state and Cardassian cosmology.