A new study has demonstrated that observations of large-scale structure formation in the universe, such as galaxies and galaxy clusters, can be a key tool to differentiate between various holographic dark energy models. Researchers utilized a combination of cosmological datasets, including Pantheon+ SN Ia, OHD, DESI DR2 baryonic acoustic oscillation data, and CMB distance prior measurements, to constrain the parameters of three specific models: HDE (Holographic Dark Energy), THDE (Thermal Holographic Dark Energy), and BHDE (Black Hole Holographic Dark Energy).

The analysis focused on the evolution of two crucial cosmological parameters: fσ₈(z) and S₈(z), which describe the growth of structures and the amplitude of matter density fluctuations, respectively. The results showed that the evolutionary curves of both fσ₈(z) and S₈(z) for the HDE and BHDE models were nearly indistinguishable. However, the curves corresponding to the THDE model consistently lay lowest. Additionally, the χ² statistic indicated that the THDE model yielded the lowest value for both fσ₈ and S₈ measurements, suggesting a better fit to observational data.

To visualize these differences, the authors constructed a diagnostic (fσ₈, S₈) plane and analyzed the trajectories of the models. In this plane, the trajectory of the THDE model was able to reach the current (fσ₈, S₈) data region, which was not the case for the other models. These findings confirm that cosmic structure formation offers a robust method to distinguish the THDE model from the HDE and BHDE models, and suggest that this approach can be extended to evaluate the viability of other holographic dark energy scenarios.