Tsallis Holographic Dark Energy model with varying gravitational constant vs $\Lambda$CDM model: statistical analysis of observational data and tensions problem

Abstract

We investigate the cosmological evolution of a flat Friedmann--Robertson--Walker Universe filled with Tsallis holographic dark energy (THDE) under the assumption that the gravitational constant $G$ varies with time according to the power-law parametrisation $d\ln G / d\ln a = \alpha_G = \mathrm{const}$. In this framework, the holographic dark energy density is given by $\rho_{\mathrm{DE}} \propto L^{2\gamma - 4}$, where $L$ is the future event horizon and $\gamma$ is the Tsallis non-additivity parameter. We study both the past and future evolution of the Universe for various values of the model parameters $C$, $\gamma$, and $\alpha_G$. The viability of the model is tested against a combination of observational data, including the Pantheon+ Type Ia supernova sample, direct Hubble parameter measurements $H(z)$, and baryon acoustic oscillation (BAO) data. Using Markov Chain Monte Carlo (MCMC) methods and Bayesian analysis tools such as the Deviance Information Criterion (DIC), the Bayes factor, and the suspiciousness metric, we perform a rigorous statistical comparison with the standard $\Lambda$CDM model. Our results show that models with a varying gravitational constant are preferred over $\Lambda$CDM. The best fit to the combined data is obtained for the THDE model with $C < 1$. Furthermore, we analyse the internal consistency of the data sets using the Index of Inconsistency, the $Q_{\mathrm{DMAP}}$ statistic, and Bayesian suspiciousness. We find that the THDE model with varying $G$ and $C < 1$ partially alleviates the tensions between different probes, reducing the significance from $\sim 7.4\sigma$ to $\sim 5.3\sigma$.