Holographic dark-energy models

Abstract

Different holographic dark-energy models are studied from a unifying point of view. We compare models for which the Hubble scale, the future event horizon or a quantity proportional to the Ricci scale are taken as the infrared cutoff length. We demonstrate that the mere definition of the holographic dark-energy density generally implies an interaction with the dark-matter component. We discuss the relation between the equation-of-state parameter and the energy density ratio of both components for each of the choices, as well as the possibility of noninteracting and scaling solutions. Parameter estimations for all three cutoff options are performed with the help of a Bayesian statistical analysis, using data from supernovae type Ia and the history of the Hubble parameter. The $\ensuremath{\Lambda}\mathrm{CDM}$ model is the clear winner of the analysis. According to the Bayesian information criterion (BIC), all holographic models should be considered as ruled out, since the difference $\ensuremath{\Delta}\mathrm{BIC}$ to the corresponding $\ensuremath{\Lambda}\mathrm{CDM}$ value is $>10$. According to the Akaike information criterion (AIC), however, we find $\ensuremath{\Delta}\mathrm{AIC}<2$ for models with Hubble-scale and Ricci-scale cutoffs, indicating, that they may still be competitive. As we show for the example of the Ricci-scale case, also the use of certain priors, reducing the number of free parameters to that of the $\ensuremath{\Lambda}\mathrm{CDM}$ model, may result in a competitive holographic model.