Updated observational constraints on interacting holographic dark energy models in a non-flat universe

Abstract In this paper, we update constraints on the Holographic Dark Energy (HDE) model and the Interacting Holographic Dark Energy (IHDE) models in a non-flat universe, building upon our previous work in which the flat HDE and IHDE models were tested using same datasets, including DESI DR2 BAO, the five-year supernovae sample from DES, CMB distance priors, observational Hubble parameter data, and the local measurement of Hubble constant. Our results indicate that in the HDE model, an open universe is supported at $$6\sigma $$ 6 σ , whereas in the IHDE models a closed universe is favored at over $$3\sigma $$ 3 σ . The model parameter c is anti-correlated with $$H_0$$ H 0 in all these models, implying that a resolution to $$H_0$$ H 0 tension by reducing the parameter c comes at the expense of a Big Rip fate. Furthermore, using AIC, BIC, DIC, and Bayes evidence, we find that within the non-flat framework, the $$\Lambda $$ Λ CDM model remains the most strongly supported by the data, while the HDE model is the most disfavored. Compared with the HDE model, the IHDE models demonstrate markedly improved agreement with the data, and the most strongly supported IHDE model is the one with the interaction term $$Q=3\beta H_{\textrm{0}}\frac{\rho _{\textrm{dm}}\rho _{\textrm{de}}}{\rho _{\textrm{dm}}+\rho _{\textrm{de}}}$$ Q = 3 β H 0 ρ dm ρ de ρ dm + ρ de .