Generalized Holographic and Ricci Dark Energy: Cosmological Diagnostics and Scalar Field Realizations

Abstract

In this work, we present two generalized formulations of the Holographic and Ricci Dark Energy (DE) models, given by ${\rho }_{GH}=3c^2{M}_{pl}^2\left[1-\epsilon \left(1-\frac{R}{H^2}\right)\right]H^2$ and ${\rho }_{GR}=3c^2{M}_{pl}^2\left[1-\eta \left(1-\frac{H^2}{R}\right)\right]R$ where $H$ and $R$ denote the Hubble parameter and the Ricci scalar, while $\epsilon$ and $\eta$ are model parameters related by $\epsilon =1-\eta$. We derived explicit analytical expressions for key cosmological quantities, including the Hubble parameter, the DE density ${\rho }_D$, the DE pressure $p_D$, the equation of state parameter of DE ${\omega }_D$ and the deceleration parameter $q$. The analysis was carried out for four distinct cases: (i) the standard model in its original formulation; (ii) the inclusion of spatial curvature; (iii) the addition of interactions between the dark sectors; and (iv) the presence of both interaction and curvature. Moreover, we also considered the limiting case of a DE Dominated Universe. To further characterize the dynamical features of the models, we investigated several diagnostic tools, namely the statefinder parameters, the $Om(z)$ diagnostic, the squared speed of the sound $v_s^2$, the cosmographic parameters and the age of the present Universe. Moreover, we established a correspondence between the DE models we studied and some scalar field theories, including tachyon, k-essence, dilaton, quintessence, Dirac-Born-Infeld, Yang-Mills and Nonlinear Electrodynamics (NLED) fields.