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

In this work, we present two generalized formulations of the Holographic and Ricci Dark Energy (DE) models, given by $ ρ_{GH} = 3c^2M^{2}_{pl} \left[ 1-ε\left(1-\frac{R}{H^2}\right) \right]H^2$ and $ρ_{GR} = 3c^2M^{2}_{pl}\left[ 1-η\left(1-\frac{H^2}{R}\right) \right]R$ where $H$ and $R$ denote the Hubble parameter and the Ricci scalar, while $ε$ and $η$ are model parameters related by $ε= 1 - η$. We derived explicit analytical expressions for key cosmological quantities, including the Hubble parameter, the DE density $ρ_D$, the DE pressure $p_D$, the equation of state parameter of DE $ω_D$ 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.