The question of the initial configuration of the Universe — did the expanding Friedmann space-time ds2 = dt2 - a2(t)dx2 tend to a singularity when extrapolated back 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 γ = 1, then the higher-derivative terms ℛ2 in the Lagrangian L dominate the Einstein–Hilbert term R/16πG in the time interval t p ≲ t ≲ 4t p , during which the action is S ≈ 25ℏ, guaranteeing the approximate validity of the classical field equations (if the compactification process is ignored), where [Formula: see text] is the Newton gravitational constant and t p is the Planck time. Under these conditions, Ruzmaĭkina and Ruzmaĭkina 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-zero 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) ≳ 5 × 1029t p . While if γ = 2, then ℛ2 never dominates R/16πG. Accordingly, we conjecture that the Universe did not bounce, irrespective of the value of γ, the absence of a prior contracting phase thus being an aspect of causality.
A class of QFTs with higher derivative field equations leading to standard dispersion relation for the particle excitations
