Emergence of cosmic space and minimal length in quantum gravity

An emergence of cosmic space has been suggested by Padmanabhan in [1]. This new interesting approach argues that the expansion of the universe is due to the difference between the number of degrees of freedom on a holographic surface and the one in the emerged bulk. In this paper, we derive, using emergence of cosmic space framework, the general dynamical equation of FRW universe filled with a perfect fluid by considering a generic form of the entropy as a function of area. Our derivation is considered as a generalization of emergence of cosmic space with a general form of entropy. We apply our equation with higher dimensional spacetime and derive modified Friedmann equation in Gauss–Bonnet gravity. We then apply our derived equation with the corrected entropy-area law that follows from Generalized Uncertainty Principle (GUP) and derive a modified Friedmann equations due to the GUP. We then derive the modified Raychaudhuri equation due to GUP in emergence of cosmic space framework and investigate it using fixed point method. Studying this modified Raychaudhuri equation leads to nonsingular solutions which may resolve singularities in FRW universe.