A cosmographic analysis of holographic dark energy models
Supriya Pan, Subenoy Chakraborty
TL;DR
This work analyzes holographic dark energy (HDE) in a flat FRW universe with interacting DE and DM, exploring two IR cutoffs: the Ricci length scale $L_R$ and the future event horizon $R_E$. It derives the evolution of the HDE density parameter $\Omega_d$ and the equation of state $\omega_d$ for three phenomenological interactions $Q=3b^2 H(\rho_m+\rho_d)$, $Q=\frac{\gamma}{H}\rho_m\rho_d$, and $Q=3\lambda H\rho_d$, obtaining analytic solutions for the Ricci-scale case and numerical results for the event-horizon case; cosmographic parameters $j,s,l,m$ are introduced and studied, especially for the Ricci-scale model. The results show that the first two interactions yield cosmographic parameters within observational bounds, while the third is disfavored, and the framework can accommodate crossing $\omega=-1$, offering a counterexample to no-go theorems and providing a geometric diagnostic for model viability. These findings underscore the utility of cosmography in discriminating holographic DE models and link IR-cutoff choices and interaction forms to observable expansion dynamics, constrained by Planck data.
Abstract
The present work deals with a detailed study of interacting holographic dark energy model for three common choices of the interaction term. Also, two standard choices of IR cut-off, namely, Ricci length scale and radius of the event horizon are considered here. Finally, the cosmographic parameters are presented both analytically and graphically.