Cosmic and growth matter analysis of deformed Hořava–Lifshitz gravity

Abstract

Hořava–Lifshitz gravity is a very fascinating proposal of modified gravity for explaining the current acceleration and other cosmic issues. In continuation to this discussion, we explore the consequences of Tsallis dark energy with Hubble and particle horizons in the framework of deformed Hořava–Lifshitz gravity for flat FRW universe. The interaction between Tsallis holographic dark energy and dark matter is also taken into account to discuss the underlying scenario. It is found that fractional dark energy density ([Formula: see text]) approaches to [Formula: see text] as redshift goes to zero (present epoch) for both cases of horizons. The cosmic parameter ([Formula: see text]) shows phantom crossing behavior in both models, i.e. it evolutes the universe from quintessence phase to phantom phase by crossing the vacuum horizon. In both cases of horizons, the deceleration supports the cosmic acceleration by exhibiting the negative values. The perturbation sound speed also favors the viability of our models through positive behavior. The coincidence parameter supports the exchange of dark matter to dark energy phenomenon through positivity. We also discuss the behavior of growth rate and growth index in the growth of matter density perturbations for both horizons. These parameters mimic the [Formula: see text]CDM behavior of the universe.