Tsallis and Rényi statistics based on H0 controversy

Abstract

Motivated by recent attempts to study the implications of Tsallis and Rényi statistics in gravitational, cosmological, and astrophysical systems, the possible relationships between $H_0$ tension and generalized statistics are explored. It is obtained that, in the light of $H_0$ tension, the energy-time uncertainty relations in Tsallis and Rényi statistics constrain the values of Tsallis and Rényi parameters. Hence, the way to find the footprints of non-extensivity in the universe is paved.