A closer look at interacting dark energy with statefinder hierarchy and growth rate of structure

TL;DR

This paper analyzes interacting dark energy models using geometrical and structure growth diagnostics, highlighting the potential of combined diagnostics to distinguish these models from the standard $\\Lambda$CDM cosmology.

Contribution

It introduces a combined diagnostic approach using statefinder hierarchy and growth rate to better differentiate interacting dark energy models from $\\Lambda$CDM.

Findings

The impact of the dark energy equation-of-state parameter $w$ is stronger than the coupling parameter $\beta$.

Distinctive features in the $S^{(1)}_3$--$\epsilon$ plane can effectively distinguish models.

The combined diagnostic $\\{S^{(1)}_3, \epsilon\}$ is promising for investigating interacting dark energy.

Abstract

We investigate the interacting dark energy models by using the diagnostics of statefinder hierarchy and growth rate of structure. We wish to explore the deviations from $\Lambda$CDM and to differentiate possible degeneracies in the interacting dark energy models with the geometrical and structure growth diagnostics. We consider two interacting forms for the models, i.e., $Q_1=\beta H\rho_c$ and $Q_2=\beta H\rho_{de}$, with $\beta$ being the dimensionless coupling parameter. Our focus is the I$\Lambda$CDM model that is a one-parameter extension to $\Lambda$CDM by considering a direct coupling between the vacuum energy ($\Lambda$) and cold dark matter (CDM), with the only additional parameter $\beta$. But we begin with a more general case by considering the I$w$CDM model in which dark energy has a constant $w$ (equation-of-state parameter). For calculating the growth rate of structure, we employ the "parametrized post-Friedmann" theoretical framework for interacting dark energy to numerically obtain the $\epsilon(z)$ values for the models. We show that in both geometrical and structural diagnostics the impact of $w$ is much stronger than that of $\beta$ in the I$w$CDM model. We thus wish to have a closer look at the I$\Lambda$CDM model by combining the geometrical and structural diagnostics. We find that the evolutionary trajectories in the $S^{(1)}_3$--$\epsilon$ plane exhibit distinctive features and the departures from $\Lambda$CDM could be well evaluated, theoretically, indicating that the composite null diagnostic $\{S^{(1)}_3, \epsilon\}$ is a promising tool for investigating the interacting dark energy models.