Comparing teh holographic principle inspired dark energy models

Abstract: In this work, we use the statefinder parameter diagnostic to the Holographic principal inspired dark energy models, taking into consideration, the Tsallis Holographic dark energy (THDE) model, the standard Holographic dark energy (HDE) model, and the R$\acute{e}$nyi holographic dark energy (RHDE) model. The evolutionary behaviour of first statefinder $r(z)$, second statefinder parameter $s(z)$, the statefinder parameter pairs $(r, s)$ and $(r, q)$ as well as the deceleration parameter $q(z)$ are plotted for comparison for the various parameter values of the respective dark energy models. In the low redshift region, it is observed from these plots that the Tsallis holographic dark energy (THDE) model and R$\acute{e}$nyi holographic dark energy (RHDE) model approach to the $\Lambda$CDM model. While for the HDE model, the evolutionary behaviour can be differentiated from the $\Lambda$CDM model in the low-redshift region. For all three dark energy models, a direct comparison in $q(z)$, $r(z)$, $s(z)$, $(r, s)$ and $(r, q)$ plane have also been done, in which the discrimination between these three models wif the $\Lambda$CDM model) may be easily seen.