Feasibility Analysis of Holographic Dark Energy Based on Generalized Entropy

In this study, we investigate the feasibility of generating holographic dark energy based on different infrared cut-offs under different generalized entropy functions. Specifically, we analyze six dark energy models formed by combining three-parameter generalized entropy and five-parameter generalized entropy with three infrared cut-offs. These three cut-offs are the Granda-Oliveros (GO) cut-off, the GO+1/H (GO-H) cut-off, and the GO+H¨\ddot HH¨ (GO-ddH) cut-off, all of which belong to the Nojiri–Odintsov cut-off category. We perform a Bayesian Markov Chain Monte Carlo (MCMC) analysis to constrain the cosmological parameters using the Pantheon+, DESI, and Compressed Planck likelihood datasets. Furthermore, the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) statistical tools are also used to compare preferences between models. The results show that the data does not favor any of the six models as much as the \LambdaCDM model. Although the maximum log-likelihood of some models is greater than that of the \LambdaCDM model, the extra parameters will cause ΔAIC > 0. Among these six models, the three-parameter entropy with GO and the five-parameter entropy with GO-ddH are significantly better than the other models, with ΔAIC values ​​of 3.16 and 18.37, respectively. The other four models all have a ΔAIC greater than 100, and our dataset also makes it difficult to distinguish them. We also investigate the evolution of the dark energy equation of state. The results show that, except for the three-parameter entropy combined with the GO model (which exhibits quintessence-like behavior), all other models display phantom crossing (inverse phantom crossing) phenomena.