Using the Kaniadakis horizon entropy in the presence of neutrinos to alleviate the Hubble and $ S_{8} $ Tensions

The $H_{0}$ tension stands as a prominent challenge in cosmology, serving as a primary driver for exploring alternative models of dark energy. Another tension arises from measurements of the $ S_{8} $ parameter, which is characterize the amplitude of matter fluctuations in the universe. In this study, we address the alleviation of both the Hubble tension and $ S_{8} $ tension by incorporating Kaniadakis horizon entropy. We investigate two scenarios to explore the impact of this entropy on cosmological parameters. In the first scenario, utilizing modified Friedmann equations through Kaniadakis entropy, we estimate the values of $H_{0}$ and $ S_{8} $. In the subsequent scenario, we introduce the neutrino term and assess its effect on mitigating the Hubble and $ S_{8} $ tensions. Our findings reveal that when considering the first scenario, the results closely align with Planck's 2018 outcomes for Hubble and $ S_{8} $ tensions. Moreover, with the inclusion of neutrinos, these tensions are alleviated to approximately 2$\sigma$, and the $ S_{8} $ value is in full agreement with the results from the KiDS and DES survey. Furthermore, we impose a constraint on the parameter $K$ in each scenario. Our analysis yields $K = 0.12\pm 0.41$ for Kaniadakis entropy without neutrinos and $K = 0.39\pm 0.4$ for the combined dataset considering Kaniadakis entropy in the presence of neutrinos. We demonstrate that the value of K may be affected by neutrino mass, which can cause energy transfer between different parts of the universe and alter the Hubble parameter value.