Comparative Observational Analysis of Barrow and Tsallis Holographic Dark Energy in Braneworld Models

Abstract

We perform a comparative observational analysis of Barrow and Tsallis holographic dark energy models within the framework of braneworld cosmology. Working in the Dvali– Gabadadze–Porrati (DGP) and Randall–Sundrum type II (RSII) scenarios, we consider the Hubble horizon as the infrared cutoff and constrain the models using Observed Hubble Data (OHD). Building upon earlier dynamical studies and a preliminary observational analysis of Barrow holographic dark energy, we employ a Bayesian Markov Chain Monte Carlo approach to obtain marginalized posterior distributions, confidence intervals and parameter correlations. Our results show that the Barrow holographic dark energy model yields wellconstrained deformation parameters in both DGP and RSII braneworlds, consistent with their theoretical bounds and exhibiting weak parameter degeneracies. In contrast, while the Tsallis holographic dark energy provides an acceptable fit to the OHD data, its normalization parameter remains weakly constrained, and the preferred values of the Tsallis exponent differ significantly from those commonly adopted in earlier dynamical analyses. These results indicate that observational constraints favor the Barrow formulation over the Tsallis one within the braneworld context considered here, and thereby highlighting the role of theoretical entropy bounds in improving the robustness of holographic dark energy models.