The hidden sector of the E-8 x E-8' heterotic superstring theory of Gross et al. can in principle contain additional "shadow" matter, interacting only gravitationally with the real world in which we live. The SU(3)(C)' x SU(2)(L)' x U(1)(Y)' shadow configuration symmetric to the standard model has been ruled out by Kolb et al. from nucleosynthesis arguments, combined with the existence of three light neutrinos. In the absence of inflation and of entropy enhancement by the out-of-equilibrium decay of an unstable particle, the same exclusion applies to the unbroken E-8' hidden gauge group, assuming thermodynamical equilibrium with the observable sector Es group, and consequently all breaking chains E-8' --> G(1) x G(2) x ..., since they can only reduce the effective number of four-dimensional degrees of freedom g(eff). The hidden sector would then appear to be in its vacuum state, which implies the absence of all condensates as well, if their potentials are positive semi-definite. In this case, and if there is no anomalous U(1) symmetry in the observable sector, the QCD axion is the model-independent axion, whose decay constant f(a) approximate to 218g(s)(2) x 10(16) GeV (where g(s)(2) is the strong-interaction coupling parameter) requires a fine-tuning of the initial value of this axion field to a(i)/f(a) less than or similar to 3 x 10(-3), in order not to overdose the Universe today, supersymmetry being broken by gauge mediation. Vice verse, if a(i)/f(a) similar to 1, then hidden-sector gaugino condensation is necessary for there to be a sufficiently massive gravitino, whose decay can increase the entropy. Astronomical microlensing observations may help to discriminate between these two cases.