Growth of Perturbations using Lambert$W$ Equation of State

TL;DR

This paper investigates how a novel Lambert$W$ function-based dark energy model influences the growth of cosmic perturbations, comparing its effects with standard cosmological models.

Contribution

It introduces and analyzes the impact of Lambert$W$ dark energy on structure formation, a novel approach not previously explored in cosmology.

Findings

Lambert$W$ dark energy significantly alters growth rates of matter perturbations.

The model's effects differ from standard $\Lambda$CDM and CPL models.

Presence of Lambert$W$ dark energy impacts matter fluctuations extensively.

Abstract

Recently, a novel equation of state (EoS) parameter for dark energy has been introduced which deals with a special mathematical function, known as the Lambert$W$ function. In this paper, we study the effect on the growth of perturbations for the Lambert$W$ dark energy model. We perform the analysis for two different approaches. In the first case we consider the universe to be filled with two different fluid components, namely, the baryonic matter component and the Lambert$W$ dark energy component, while in the second case we consider that there is a single fluid component in the universe whose equation of state parameter is described by the Lambert$W$ function. We then compare the growth rates of Lambert$W$ model with that for a standard $\Lambda$CDM model as well as the CPL model. Our results indicate that the presence of Lambert$W$ dynamical dark energy sector changes the growth rate and affects the matter fluctuations in the universe to a great extent.