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.
Highlights
The name dark energy started to be used by [1] in order to explain both the expansion and both the acceleration of the universe
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
The term wCDM has been introduced to classify the case of constant equation of state and we will use in the following wzCDM to classify the variable equation of state
Summary
The name dark energy started to be used by [1] in order to explain both the expansion and both the acceleration of the universe. The above historical samples allowed to derive the cosmological parameters for the expanding and accelerating universe. The above observations can be done up to a limited value in redshift z ≈ 1.7 , we, speak of evaluation of the distance modulus at low redshift This limited range can be extended up z ≈ 8 , the high redshift region, analyzing the Gamma-Ray Burst (GRB) and, as an example, [11] has derived the distance modulus for 59 calibrated highredshift GRBs, the so-called “Hymnium” GRBs sample.
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