Alleviating both H_0 and σ _8 tensions in Tsallis cosmology

We present how Tsallis cosmology can alleviate both H_0 and 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 δ that quantifies the departure from standard entropy. We show that for particular 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 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 σ _8 tension is also solved. These features act as a significant advantage of Tsallis modified cosmology.