Interacting Tsallis and Rényi holographic dark energy with hybrid expansion law

The manuscript presents the dynamics of Tsallis holographic dark energy (THDE) and Rényi 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 ${\omega }_{de}-{\omega }_{de}^{\prime }$ plane and find that the plane lies in the freezing region for the THDE model and in the thawing region for the RHDE model.