Recursive Heaviside step functions and beginning of the universe

Abstract

This article introduces recursive Heaviside step functions, as a potential of the known universe, for the first time in the history of mathematics, science, and engineering. In modern cosmology, various bouncing models have been suggested based on the postulation that the current universe is the result of the collapse of a previous universe. However, all Big Bounce models leave unanswered the question of what powered inflation. Recursive Heaviside step functions are analyzed to represent the warpage of spacetime during the crunch-bounce transition. In particular, the time shift appeared during the transition is modeled in the form of recursive Heaviside step functions and suggested as a possible answer for the immeasurable energy appeared for the Big Bounce.