Cosmology of a generalized version of holographic dark energy and reconstruction of different scalar field models

In this paper, we consider a Dark Energy (DE) model which energy density ρ _D is a function of the Hubble parameter H squared and of the first and second time derivatives with respect to the cosmic time t of H and is just a specific case of Nojiri-Odintsov holographic DE (Nojiri and Odintsov, 2006 Gen. Relativ. Gravit. 38, 1285). Moreover, this model is characterized by three parameters which are the proportional coefficients of the three terms forming the DE model. We derive the expressions of the energy density of DE ρ _D, the pressure of DE p _D, the equation of State (EoS) parameter of DE w _D and the deceleration parameter q for different sets of constraints. We also derive the expression of the evolutionary forms of the fractional energy densities of DE, DM and curvature parameter. We also study the behavior of w _D, H, the scale factor a and q in the limiting case of a flat Universe. Finally, we establish a correspondence between the generalized version of holographic dark energy model and the tachyon, the k-essence, the dilaton and the quintessence scalar field models. It has been observed that the models are stable against small perturbations as indicated by positive squared speed of sound. Also, the possibility of avoidance of Big-Rip jeopardy has been observed. (paper)