Ricci-cubic holographic dark energy: Confronting observations, stability and the cosmic coincidence problem

In this work, we constrain the parameter space of the Ricci-Cubic Holographic Dark Energy (RCHDE) model using several observational datasets, including Hubble parameter measurements, cosmic chronometer (CC) data, Baryon Acoustic Oscillation (BAO) data, and recent DESI observations. The RCHDE model is constructed from a cubic curvature invariant formed through cubic contractions of the Ricci and Riemann tensors. To estimate the model parameters, we employ the Markov Chain Monte Carlo (MCMC) sampling technique within a Bayesian inference framework. The resulting likelihood contours provide both marginalized and joint posterior distributions of the model parameters. The best-fit cosmological evolution predicted by the RCHDE model is reconstructed and compared with observational H(z) measurements as well as with the standard ΛCDM cosmological model. The best-fit value obtained in our model exhibits a moderate Hubble tension of approximately 2.3σ with respect to the reference value for ΛCDM. While this indicates a noticeable discrepancy, it remains significantly lower than the ∼ 5σ tension typically reported between early- and late-Universe measurements, suggesting a partial alleviation of the tension. In addition to the statistical parameter estimation, we perform an enhanced machine learning analysis using observational Hubble parameter data. Several supervised regression algorithms are implemented to reconstruct the expansion history of the universe and to test the predictive capability of the RCHDE model from a data-driven perspective. Various graphical analyses are presented to illustrate the performance of the machine learning models. The results demonstrate a strong consistency between the predictions of the machine learning models, the theoretical RCHDE model, and the observational data. We have done a comparative stability analysis between different holographic dark energy models using the squared speed of sound, where it is seen that the RCHDE model does not have any upper hand over its counterparts. Finally, the cosmic coincidence problem is tested to compare the efficiency of the RCHDE model in comparison to other models. It is found that the RCHDE model produced a significant alleviation to the cosmic coincidence problem, outshining its counterparts.