Are dark energy models with variable EoS parameter $w$ compatible with the late inhomogeneous Universe?

TL;DR

This paper investigates whether dark energy models with a variable equation of state parameter $w$ are compatible with the late inhomogeneous Universe, using scalar perturbations within the mechanical approach, and finds that certain models are incompatible.

Contribution

The study develops a system of equations for scalar perturbations with arbitrary dark energy EoS and demonstrates the incompatibility of variable $w$ models with late Universe inhomogeneities.

Findings

Constant $w$ models favor the cosmological constant.

Variable $w$ models with linear parametrizations are incompatible with scalar perturbations.

The mechanical approach effectively tests dark energy models against late Universe inhomogeneities.

Abstract

We study the late-time evolution of the Universe where dark energy (DE) is presented by a barotropic fluid on top of cold dark matter (CDM). We also take into account the radiation content of the Universe. Here by the late stage of the evolution we refer to the epoch where CDM is already clustered into inhomogeneously distributed discrete structures (galaxies, groups and clusters of galaxies). Under this condition the mechanical approach is an adequate tool to study the Universe deep inside the cell of uniformity. More precisely, we study scalar perturbations of the FLRW metric due to inhomogeneities of CDM as well as fluctuations of radiation and DE. For an arbitrary equation of state for DE we obtain a system of equations for the scalar perturbations within the mechanical approach. First, in the case of a constant DE equation of state parameter $w$, we demonstrate that our method singles out the cosmological constant as the only viable dark energy candidate. Then, we apply our approach to variable equation of state parameters in the form of three different linear parametrizations of $w$, e.g., the Chevallier-Polarski-Linder perfect fluid model. We conclude that all these models are incompatible with the theory of scalar perturbations in the late Universe.