How did the Universe begin?

摘要

The question of the initial configuration of the Universe - did the expanding Friedmann space-time ds(2) = dt(2) -a(2)(t)dx(2) tend to a singularity when extrapolated bade in time, or was there a turning point, indicating a previous phase of contraction? - is re-examined in the context of the heterotic superstring theory of Gross et al. If the adiabatic index tends to the value gamma = 1, then the higher-derivative terms R-2 in the Lagrangian L dominate the Einstein-Hilbert term R/16 pi G in the time interval t(P) less than or similar to t less than or similar to 14t(P), during which the action is S approximate to 25 (h) over bar, guaranteeing the approximate validity df the classical field equations (if the compactification process is ignored), where G = t(P)(2) is the Newton gravitational constant and tp is the Planck time. Under these conditions, Ruzmaikina and Ruzmaikin have shown, for a flat three-space with K = 0, that the initial singularity can only be avoided at all if there is a spin-aero tachyon, a conclusion modified by Barrow and Ottewill if K = +/-1. We have previously shown, however, that the theory is tachyon-free, and have argued that K has to vanish for the existence of a well-defined, quantum-mechanical ground state. Also, if there is no inflation, the radius function is always much too large for the terms in K to exert any effect, a(t) greater than or similar to 5 x 10(29)t(P). While if gamma = 2, then R-2 never dominates R/16 pi G. Accordingly, we conjecture that the Universe did not bounce, irrespective of the value of gamma, the absence of a prior contracting phase thus being an aspect of causality. [References: 33]