Generalized logarithmic modification of Barrow–Tsallis entropy can alleviate the Hubble tension

This study investigates the generalized Barrow–Tsallis entropy, characterized by the quantum-gravitational deformation parameter $\Delta$, the Tsallis nonextensivity parameter $q$, and the logarithmic correction parameter $\alpha$, as a framework for addressing the Hubble tension within a modified cosmological model. By incorporating the Barrow entropy, $S\propto A^{\Delta }$, and Tsallis entropy, $S_q=\frac{A}{4G}+\tilde{\alpha }{ln}_q\frac{A}{4G}+\tilde{\beta }$, we derive modified Friedmann equations in a Friedmann–Robertson–Walker (FRW) universe, introducing an effective dark energy component. The model is constrained using a comprehensive combination of observational datasets, including Planck 2018 Cosmic Microwave Background (CMB) data, Baryon Acoustic Oscillations (BAO), Cosmic Chronometers (CC), Pantheon Supernovae, and Planck lensing data. Our analysis reveals that the inclusion of these datasets significantly mitigates the Hubble tension, achieving a $1.21\sigma$ agreement with Planck 2018 and $0.98\sigma$ with the R22 local measurement. The parameter $\alpha$ indicates subtle deviations from classical entropy, while $\Delta$ is tightly constrained to $\Delta <0.002$, suggesting minimal quantum-gravitational corrections on cosmological scales. Furthermore, the Tsallis parameter $q$ stabilizes at $q\approx 0.41$, demonstrating the robustness of the model in fitting observational data. This work demonstrates that the generalized entropy framework serves as a compelling alternative to the standard $\Lambda$CDM model, offering competitive performance in reconciling the Hubble tension and explaining late-time cosmic acceleration.