  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.
