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

TL;DR

This work introduces two generalized dark energy densities, GH and GR, defined by $\rho_{GH}=3c^2M_{pl}^2[1-\varepsilon(1-R/H^2)]H^2$ and $\rho_{GR}=3c^2M_{pl}^2[1-\eta(1-H^2/R)]R$, linked by $\varepsilon=1-\eta$. The authors derive analytic expressions for the Hubble rate, DE density and pressure, EoS, and deceleration parameter, exploring four setups: standard, with curvature, with interaction, and with both curvature and interaction, and they also analyze the DE-dominated limit. A broad diagnostic suite is employed, including statefinder parameters $\{r,s\}$, the $Om(z)$ diagnostic, the squared sound speed $v_s^2$, cosmographic parameters, and the Universe’s age, complemented by a reconstruction of the generalized models into various scalar-field theories (tachyon, k-essence, dilaton, quintessence, DBI, YM, NLED). The paper finds rich phenomenology ranging from near-$\Lambda$CDM-like behavior to distinctly dynamical DE, controlled by parameters $c^2$, $\varepsilon$, $\eta$, and the interaction strength $d^2$, with explicit DE-dominated limits and diverse scalar-field realizations. These results offer diagnostic and model-building avenues to confront GH/GR holographic-dark-energy scenarios with observations.

Abstract

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.

Figures (21)

• Figure 1: Comparison of the three plots of $\omega_{D_{GH}}(x)$.
• Figure 2: Comparison of the three cases for the deceleration parameter $q_{GH}(x)$.
• Figure 3: Comparison of the three plots of $\omega_{D_{GH},k}(x)$.
• Figure 4: Comparison of the three cases for the deceleration parameter $q_{GH,k}(x)$.
• Figure 5: Comparison of the three plots of $\omega_{D_{GH},I}(x)$.