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We report how to alleviate both the $H_0$ and $\sigma_8$ tensionssimultaneously within $f(T)$ gravity. In particular, we consider theparametrization $f(T)=-T-2\Lambda/M_P^2+\alpha T^\beta$, where two out of thethree parameters are independent. This model can efficiently fit observationssolving the two tensions. To our knowledge, this is the first time where amodified gravity theory can alleviate both $H_0$ and $\sigma_8$ tensionssimultaneously, hence, offering an additional argument in favor ofgravitational modification.

Solving both $H_0$ and $\sigma_8$ tensions in $f(T)$ gravity