Diagnosing $\Lambda$HDE model with statefinder hierarchy and fractional growth parameter

TL;DR

This paper evaluates the $ ext{Lambda}$HDE dark energy model using various diagnostic tools to understand how parameters influence cosmic evolution and to improve model discrimination.

Contribution

It applies statefinder hierarchy, fractional growth parameter, and composite null diagnostic to analyze the impacts of key parameters on the $ ext{Lambda}$HDE model, enhancing diagnostic methods.

Findings

Different $ ext{Omega}_{ ext{Lambda}0}$ values only quantitatively affect evolution.

Different $c$ values qualitatively change evolution.

CND provides stronger diagnostic power than single tools.

Abstract

Recently, a new dark energy model called $\Lambda$HDE was proposed. In this model, dark energy consists of two parts: cosmological constant $\Lambda$ and holographic dark energy (HDE). Two key parameters of this model are the fractional density of cosmological constant $\Omega_{\Lambda0}$, and the dimensionless HDE parameter $c$. Since these two parameters determine the dynamical properties of DE and the destiny of universe, it is important to study the impacts of different values of $\Omega_{\Lambda0}$ and $c$ on the $\Lambda$HDE model. In this paper, we apply various DE diagnostic tools to diagnose $\Lambda$HDE models with different values of $\Omega_{\Lambda0}$ and $c$; these tools include statefinder hierarchy \{$S_3^{(1)}, S_4^{(1)}$\}, fractional growth parameter $\epsilon$, and composite null diagnostic (CND), which is a combination of \{$S_3^{(1)}, S_4^{(1)}$\} and $\epsilon$. We find that: (1) adopting different values of $\Omega_{\Lambda0}$ only has quantitative impacts on the evolution of the $\Lambda$HDE model, while adopting different $c$ has qualitative impacts; (2) compared with $S_3^{(1)}$, $S_4^{(1)}$ can give larger differences among the cosmic evolutions of the $\Lambda$HDE model associated with different $\Omega_{\Lambda0}$ or different $c$; (3) compared with the case of using a single diagnostic, adopting a CND pair has much stronger ability to diagnose the $\Lambda$HDE model.