The R\'{e}nyi holographic dark energy model in Chern-Simons gravity: some cosmological implications

In this paper, we study R\'{e}nyi holographic dark energy model in the context of Chern Simons (CS) modified gravity theory. Different cosmological parameters such as energy density, deceleration parameter, equation of state, square of sound speed and cosmological plane are discussed using FRW metric. Two separate solutions of CS field equations arose. The R\'{e}nyi HDE model showed the transition from deceleration to acceleration phase which is fully consistent with the observational data while in the second case it represented a decelerated phase of expansion only. In fact, EoS illustrates the era of dominance of the universe by certain components. Our results predicted that the universe is under the influence of dark energy as EoS showed accelerated expansion phase. On the other hand case two advocated the influence of $\Lambda$ CDM. In both cases, $\omega <0,\omega^{\prime}<0$ indicated that the R\'{e}nyi HDE model is in the freezing region and cosmic expansion is more accelerating in the context of CS modified gravity. It is also observed that the value of $\nu^2_s$ is positive $\forall z\in \Re$ a sufficient condition for the stability of the system. Hence it is concluded that the R\'{e}nyi HDE model is supported by the results of general relativity in the framework of CS modified gravity.