We present how Tsallis cosmology can alleviate both H0β and Ο8β
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 Ξ΄ that quantifies the departure from
standard entropy. We show that for particular Ξ΄ choices we can obtain a
phantom effective dark energy, which is known to be one of the sufficient
mechanisms that can alleviate H0β 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 Ο8β tension is also
solved. These features act as a significant advantage of Tsallis modified
cosmology.Comment: 14 pages, 4 figure