The hidden sector of the E8×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 × SU (2)′ L × 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 E6 group, and consequently all breaking chains E′8→ G1×G2×⋯, 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 [Formula: see text] (where [Formula: see text] is the strong-interaction coupling parameter) requires a fine-tuning of the initial value of this axion field to ai/fa≲3×10-3, in order not to overclose the Universe today, supersymmetry being broken by gauge mediation. Vice versa, if ai/fa~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.
Focus point gauge mediation without a severe fine-tuning
