Note on Granda-Oliveros Holographic Dark Energy

This article revisits Granda-Oliveros holographic dark energy (GOHDE) model, explores the features of the parameter space and shows that its ability to explain the late-time acceleration is only due to the integration constant that appears by construction. We show that the GOHDE behaves like the dominant energy component and naturally behaves like dark energy in the late phase. In the matter-dominated period, it acts like pressureless matter and exhibits radiation-like behaviour in the very early stages. Adjusting the free parameters could subdue or enhance these characteristics. Depending on the parameters, GOHDE can act similarly to concordance, phantom or quintessence-like dark energies with singular equation of states. From the point of local observations, we show that the GOHDE model is observationally indistinguishable from $w$CDM and encompasses $\Lambda$CDM as a specific case. Our analysis reveals that while a departure from $\Lambda$CDM could account for late-time acceleration, it falls short of a consistent description of the entire cosmic history. Furthermore, we utilize various datasets, including OHD, Pantheon, CMB Shift parameter, BAO, and QSO, to constrain the free parameters of the GOHDE model. Our analysis indicates that the best fit, assuming the GO cut-off, aligns with the $\Lambda$CDM model. Additionally, we use statistical quantifiers such as AIC, BIC, and $\chi^2$ to test the model's goodness with various data combinations and estimate the Bayes factor to contrast the models. Our study suggests that the standard GOHDE model is equally likely as the $\Lambda$CDM model, ultimately favouring the latter, with $\beta=0.686^{+0.048}_{-0.044}$ and $w{z_0}=-0.988^{+0.042}_{-0.044}$. Given the current observations, we conclude that, for a flat universe, the $\Lambda$CDM case is statistically the best and probably the only consistent solution from the GOHDE construction.