Abstract:

In the first part of my talk I explain how to unify all three
dark components of the universe: inflation, dark energy and dark matter
within realistic model of F(R) gravity. Dark matter is described by the
axion and non-minimal coupling of axion with gravity is assumed. In the
second part of my talk I will introduce generalised entropy construct which
gives all known entropies Tsallis, Renyi, Loop Gravity one, Barrow, etc as
particular examples. The application of generalised entropy for modified
FRW cosmology and BH thermodynamics is discussed. It is shown that most
consistent BH thermodynamics should be yet described by Bekenstein-Hawking
entropy.