Studying Thermal and Dynamical Stability of Interacting Rényi and Tsallis Holographic Dark Energy Models in LTB Inhomogeneous Universe

Abstract This work aims to investigate the different stability conditions of two scenarios of the inhomogeneous Lemaitre–Tolman–Bond model of the universe with holographic dark energy. We considered the Rényi and Tsallis holographic models of interacting dark energy. These holographic models are investigated using the IR cutoff that equals the Hubble horizon. Various stability conditions of these models have been investigated to understand how much these models can tell us about the recent and future epochs of the universe in comparison with the cosmological constant model, or ΛCDM model. The conditions of violating the cosmological energy conditions have been studied. The evolution of the entropy and its first and second derivatives have been calculated and plotted for these holographic models. This gives an idea of how far these models satisfy the generalized second law of thermodynamics and hence have thermodynamical stability. The dynamical stability is studied for these evolved models, which give us glimpses of the dynamical stability at different phases of its evolution. We focus on investigating the stability in recent and near future times up to z ≤ −4. Further investigation of stability has been obtained by studying the evolved sound speed squared parameter for these models, which gave us a final and decisive evaluation of the stability of these models.