Parameterization of the Equation of State and the expansion history of the very recent universe

TL;DR

This paper analyzes the parameterization of the equation of state for the universe's recent expansion, showing that a linear approximation suffices and providing power series expansions useful for precision cosmology.

Contribution

It demonstrates that a linear approximation to the Maclaurin series effectively models the recent universe's expansion, and offers comprehensive power series expansions for key cosmological quantities.

Findings

Linear approximation to the Maclaurin series is effective.

Power series for energy density and Hubble parameter are derived.

Complete analysis of parameterizations for high redshift is provided.

Abstract

Motivated by a nice result shown by E. Linder, a detailed discussion on the choice of the expansion parameters of the Maclaurin series for the equation of states of a perfect fluid is presented in this paper. We show that their nice recent result is in fact a linear approximation to the full Maclaurin series as a power series of the parameter $y=z/(1+z)$. The power series for the energy density function, the Hubble parameter and related physical quantities of interest are also shown in this paper. The method presented here will have significant application in the precision distance-redshift observations aiming to map out the recent expansion history of the universe. In addition, a complete analysis of all known advantageous parameterizations for the equation of states to high redshift is also presented.