Holographic Dark Energy with Modified Chaplygin Gas and Scalar Field in (2 + 1)−Dimensional Space-time

Abstract

In this paper, we generalized the work of Sheykhi (2011) and Ghose (2014) and establish the connection between Holographic Dark energy interacting with modified Chaplygin gas and then obtain the evolution of holographic dark energy with corresponding equation of state. In the first part of the paper, we have generalized the work of Sheykhi (2011) by choosing Hubble radius as the system’s IR cut-off and constructing the analytical form of the potentials as a function of scalar fields, namely V = V (ϕ) as well as this dynamics of the scalar fields as a function of time, namely ϕ = ϕ(t) then we have implemented the connection between Holographic dark energy and scalar fields model including quintessence, tachyon, K−essence and dilaton energy density in a (2+1)−dimensional spacetime FRW universe. In the second part of the paper, we have generalized the work of Ghose (2014) and investigate holographic dark energy (HDE) correspondence of interacting Modified Chaplygin Gas (MCG), and obtained evolution of the HDE with the corresponding equation of state. Considering the present value of the density parameter a stable configuration is found which accommodates Dark Energy (DE). We note a connection between DE and Phantom fields. It reveals that the DE might have evolved from a Phantom state in the past. We also obtained the stability of the model and analyzed the physical and geometrical interpretations of the cosmological model with reference to the (2 + 1)−dimensional spacetime.