Cosmological implications of vacuum energy in Rastall theory

Abstract

In this paper, we study the cosmic evolution of the holographic dark energy (HDE) model with the Hubble radius as the IR cut-off in the Rastall theory and study its dynamical behavior by two different approaches. In the first approach, we consider the vacuum energy as a candidate for dark energy, HDE, by using Cohen formulation. In the second approach we assume DE as a combination of the Rastall term and vacuum energy. We calculate the cosmological parameters, such as: equation of state, deceleration and the dimensionless density parameters of the models in both non-interacting and interacting cases for both approaches. Our studies show that, in the first approach HDE model in Rastall gravity can explain the current accelerated Universe even without interaction between two dark sectors. But the dimensionless density parameter model becomes a constant. Therefore we introduce the second approach that its dimensionless density parameter is dynamic and its evolution behavior is in agreement with the recent observational data. We have also find that in this model the Universe has a transition from the decelerated phase to accelerated phase at the redshift which is in the agreement with the cosmological observation. Also, we investigate the classical stability of