Different horizon cut-offs for Tsallis, Rényi and Sharma-Mittal holographic dark energies in Hořava-Lifshitz gravity

This study evaluates the cosmic expansion history of the universe using Tsallis, Rényi and Sharma-Mittal holographic dark energy models in a non-flat universe. The modified field equations for logarithmic and power law entropy corrected models have been investigated in Hořava-Lifshitz gravity. We suppose the universe is filled with dark energy and interacting cold dark matter. Considering the Hubble horizon and Granda-Oliveros (GO) as infrared cut-offs, we analyze the cosmological implication of the equation of state parameter, squared sound speed, and ${\omega }_d\text{–}{\omega }_d^{\prime }$ phase plane graphically during the cosmic evolution. By the equation of state parameters, we see how the universe evolved at different stages in the models we consider. We obtain the thawing or freezing regions by analyzing the phase plane ${\omega }_d\text{–}{\omega }_d^{\prime }$. We also demonstrate the classically stable or unstable behavior of the considered models by studying the squared sound speed parameter.