Barotropic fluid compatible parametrizations of dark energy

Dalibor Perković,Hrvoje Štefančić

doi:10.1140/epjc/s10052-020-8199-9

Dalibor Perković, Hrvoje Štefančić

Open Access

https://doi.org/10.1140/epjc/s10052-020-8199-9

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Abstract

Parametrizations of equation of state parameter as a function of the scale factor or redshift are frequently used in dark energy modeling. The question investigated in this paper is if parametrizations proposed in the literature are compatible with the dark energy being a barotropic fluid. The test of this compatibility is based on the functional form of the speed of sound squared, which for barotropic fluid dark energy follows directly from the function for the Equation of state parameter. The requirement that the speed of sound squared should be between 0 and speed of light squared provides constraints on model parameters using analytical and numerical methods. It is found that this fundamental requirement eliminates a large number of parametrizations as barotropic fluid dark energy models and puts strong constraints on parameters of other dark energy parametrizations.

Highlights

Ous alternatives have been proposed to both dark matter and dark energy, frequently as a modification of gravitational interaction at scales from galactic to cosmic [13,14,15]
Parametrizations of equation of state parameter as a function of the scale factor or redshift are frequently used in dark energy modeling
The test of this compatibility is based on the functional form of the speed of sound squared, which for barotropic fluid dark energy follows directly from the function for the Equation of state parameter

Summary

Introduction

Various models of dark energy have been proposed that available observational data cannot efficiently discriminate. This approach simplifies the analysis of DE dynamics and allows the analysis of physically interesting w(a) functions Such parametrizations may constitute a phenomenological approach of their own to the modeling of dark energy, their main purpose is the simplification of the fits to the observational data. For known w(a) one can obtain cs2(a) from (3) and model parameters for which 0 ≤ cs2(a) ≤ 1 is satisfied for the entire past cosmic expansion, i.e. for the entire [0, a0] interval In this way we can select w(a) parametrizations which are suitable for the description of barotropic fluid dark energy as those for which the condition on speed of sound squared is satisfied at least for some model parameters. In the “Appendix” we bring the analytical solution for the Chevallier–Polarski–Linder (CPL) model [20,21]

Analytical results

General analytical approach

Numerical results

Discussion and conclusions