Alleviating both $$H_0$$ H 0 and $$\sigma _8$$ σ 8 tensions in Tsallis cosmology

Abstract We present how Tsallis cosmology can alleviate both $$H_0$$ H 0 and $$\sigma _8$$ σ 8 tensions simultaneously. Such a modified cosmological scenario is obtained by the application of the gravity-thermodynamics conjecture, but using the non-additive Tsallis entropy, instead of the standard Bekenstein–Hawking one. Hence, one obtains modified Friedmann equations, with extra terms that depend on the new Tsallis exponent $$\delta $$ δ that quantifies the departure from standard entropy. We show that for particular $$\delta $$ δ choices we can obtain a phantom effective dark energy, which is known to be one of the sufficient mechanisms that can alleviate $$H_0$$ H 0 tension. Additionally, for the same parameter choice we obtain an increased friction term and an effective Newton’s constant smaller than the usual one, and thus the $$\sigma _8$$ σ 8 tension is also solved. These features act as a significant advantage of Tsallis modified cosmology.