Entropic force and bouncing behaviour in $\hat{I}º$-Minkowski space-time

Abstract

We generalise the entropic force description of gravity into $\hat{I}º$-Minkowski space-time and derive the $\hat{I}º$-deformed corrections to the Newton's gravitational force. Using this we show the appearance of logarithmic correction as the first order $\hat{I}º$-deformed correction term to Bekenstein-Hawking entropy. Further we also derive the $\hat{I}º$-deformed Friedmann equations and study the evolution of scale factor in $\hat{I}º$-deformed space-time. Finally we show that the $\hat{I}º$-deformation parameter avoids the initial singularity in early universe by providing a bounce behaviour for the case of spatially flat and closed universe.