Within the framework of entropic cosmology, several variants of the model of the Universe evolution based on the Friedman-Robertson-Walker (FRW) equation system are considered, reconstructed taking into account a new modification of the Kaniadakis entropy at the cosmological horizon. The modification is carried out by replacing the Bekenstein-Hocking entropy in the dual expression of the Kaniadakis entropy (in which all states have the same probability) by the Barrow entropy associated with the transformation of the horizon of the Universe surface due to quantum-gravitational effects. As a result, various cosmological scenarios of the accelerated expansion of the Universe on the basis of the reconstructed FRW equations containing an additional force term depending on two free parameters of the model are obtained: the deformation parameter κ of the Kaniadakis entropy, which is responsible for taking into account the peculiarities of space-time, due to the long-range nature of gravitation, and the deformation parameter δ of the Barrow entropy, which is responsible for the fractal structure of the cosmological horizon surface, associated with the action of gravitational-quantum effects.
A.V. Kolesnichenko (Wed,) studied this question.