Generalized Holographic and Ricci Dark Energy Models

Abstract

In this paper, we consider generalized holographic and Ricci dark energy models where the energy densities are given as ${\rho }_R=3c^2{M}_{pl}^{2}Rf(H^2/R)$ and ${\rho }_h=3c^2{M}_{pl}^2{H}^{2}g(R/H^2)$ respectively, here $f(x),g(y)$ are positive defined functions of dimensionless variables $H^2/R$ or $R/H^2$. It is interesting that holographic and Ricci dark energy densities are recovered or recovered interchangeably when the function $f(x)=g(y)\equiv 1$ or$f=g\equiv Id$ is taken respectively (for example $f(x),g(x)=1-\epsilon (1-x)$, $\epsilon =0\text{or}1$ respectively). Also, when $f(x)\equiv xg(1/x)$ is taken, the Ricci and holographic dark energy models are equivalents to a generalized one. When the simple forms $f(x)=1-\epsilon (1-x)$ and $g(y)=1-\eta (1-y)$ are taken as examples, by using current cosmic observational data, generalized dark energy models are researched. As expected, in these cases, the results show that they are equivalent ($\epsilon =1-\eta =1.312$) and Ricci-like dark energy is more favored relative to the holographic one where the Hubble horizon was taken as an IR cut-off. And, the suggestive combination of holographic and Ricci dark energy components would be $1.312R-0.312H^2$ which is $2.312H^2+1.312\dot{H}$ in terms of $H^2$ and $\dot{H}$.

10 pages, 3 figures

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