Accelerating universe via entropic models

Abstract

In this work, we propose new entropic force models by utilizing the non-extensive Tsallis entropy with a dimensionless parameter $\lambda$, which quantifies non-extensivity, and the Barrow entropy with quantum-gravitational deformation, which is quantified by a free parameter $\Delta$. We consider the universe as a sphere covered by the Hubble horizon. We have defined the Bekenstein entropy and Hawking temperature on the Hubble horizon by using the idea of Hawking and Bekenstein. We investigate the cosmological consequences of the proposed entropic force models and study the late time accelerating expansion of the universe. Although these models can describe the late time acceleration of the universe and the parameters $\lambda$ and $\Delta$ show satisfactory behavior by themselves. The parameter $\lambda$, and $\Delta$ ranges $0\le \lambda \le 1$ and $0<\Delta \le 1$. This will be done by usnig the non-additive Tsallis entropy and Barrow entropy. In addition, the comparative analysis between Tsallis and Barrow for single-fluid dominated universe is also discussed. We investigate that the expansion of the universe is uniform as it was for the cases for Bekenstein and dark energy. Tsallis and Barrow entropy will be reduced to Bekenstein entropy for the certain limits of $\lambda$ and $\Delta$.