Interacting Tsallis and R\'enyi Holographic Dark Energy with Hybrid Expansion Law

Abstract

The manuscript presents the dynamics of Tsallis holographic dark energy (THDE) and R\'enyi holographic dark energy (RHDE) prescribed by a non-linear interaction in the FRW spacetime and for a scale factor evolving with a composite power law-exponential (hybrid) form. To construct the energy densities of these holographic dark energy models, I assume the Hubble cutoff to be the IR limit. I find that the deceleration parameter undergoes a signature flipping at a redshift $z$ consistent with observations. The EoS parameter $\omega_{de}$ for both the HDE models exhibit quite contrasting dynamical behavior despite assuming values close to $-1$ at $z=0$ and therefore consistent with current observations. Next, I find the squared sound speed $c_{s}^{2}$ to be positive for the THDE model ensuring stability against perturbations, whereas for the RHDE model, $c_{s}^{2}<0$ implying instability against perturbations. Furthermore, I analyzed the evolutionary behavior of the EoS parameter of the HDE models by constructing the $\omega_{de}-\omega_{de}^{'}$ plane and find that the plane lies in the freezing region for the THDE model and in the thawing region for the RHDE model.