Modeling the dynamic evolution of the Universe under the action of the entropic force associated with the modified Sharma-Mittal entropy

Using the Verlind formalism, the paper considers several scenarios of the evolution of the Friedman-Robertson-Walker Universe, which arise in the framework of entropic cosmology based on the formulated new modification of the Sharma-Mittal entropy. The research, carried out in the framework of non-Gaussian statistical theory, uses several entropies associated with the surface of the horizon of the Universe due to the holographic information stored there. A set of new generalized Friedmann equations is obtained, in which, instead of the cosmological constant, control forces appear based on the Bekenstein-Hawking, Tsallis-Chirto and Barrow entropies, as well as modified Sharma-Mittal and Renyi entropies containing additional nonextensity parameters. The proposed approach, associated with the use of probabilistic nonextensive aspects of the Hubble horizon of the surface of the Universe, meets all the basic requirements for thermodynamic modeling of the dynamic behavior of outer space without involving the concept of dark energy.