Entropic Cosmology Based on Kaniadakis Dual Entropy on the Cosmological Horizon of the Universe

Within the framework of entropic cosmology, several variants of a model describing the evolution of the Universe are considered, based on the Friedmann–Robertson–Walker (FRW) system of equations reconstructed taking into account a new modification of the Kaniadakis entropy at the cosmological horizon. The modification is carried out by replacing the Bekenstein–Hawking 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 κ of the Barrow entropy, which is responsible for the fractal structure of the cosmological horizon surface, associated with the action of gravitational-quantum effects. The presence of two free parameters allows us to obtain new variants of driving forces in the FRW equations, which cause a deviation from the “standard” Bekenstein–Hawking holographic model and thus lead to a more accurate approximation to reality. The proposed approach meets the known requirements for thermodynamic modeling of the dynamical evolution of the Universe without involving the concept of hypothetical dark energy and based on the use of anti-gravity entropic forces. The obtained results show that the proposed entropic formalism can open additional opportunities for deeper insight into the nature of space-time and fractal properties of the Universe horizon.