Sub-Planckian Black Holes of the Variable Energy Density, Discretization of Spacetime and Modified Friedmann Equations

A model of a three-dimensional dynamic quantum vacuum defined by a fundamental variable energy density, where microphysics and macrophysics emerge from elementary sub-Planckian black holes with a size of order of a generalized Compton wavelength that unifies the standard Compton wavelength and Schwarzschild radius, is developed.The granular features of the texture of the sub-Planckian black holes at their generalized Compton wavelength are explored.Modified Friedmann equations associated with the sub-Planckian black holes of the variable energy density are introduced and cosmological consequences are derived in the picture of a cyclic universe.This approach avoids the presence of singularities and allows an unifying treatment of the different phases of the evolution of the universe.