Cosmogenesis and the tipping pencil analogy

Abstract

We present a toy model and scenario for cosmogenesis which provides an interesting rationale for the spatial flatness of the universe. The basic assumptions are that the cosmological scale factor obeys the standard Friedmann equation of general relativistic cosmology and that the equation is dominated by a cosmological constant term and a curvature term. The dynamics of the universe is then similar to that of a tipping pencil. The scale factor cannot remain at an unstable initial value of zero and must increase according to the uncertainty principle. If it is also assumed that the universe expands at the minimum asymptotic rate consistent with the uncertainty principle, the result is exact spatial flatness, rather than the near flatness obtained in standard inflation theory.