Dark matter, mirror world, and E 6 unification

Abstract

The idea that the ordinary (O) and mirror (M) worlds exist simultaneously is developed. It is shown that, in the case of a violated mirror parity (MP), the renormalization-group evolution of the coupling constants, which is represented in the O world by the dependence αi−1 (µ) (µ is an energy variable), is not identical to the evolution of the coupling constants α′i−1(µ) in the M world. Here, the index i labels the symmetry group under consideration, while a dash labels quantities defined in the M world. It is assumed that E6 unification predicted by superstring theory restores MP at the unification scale MSGUT ∼ 1018 GeV, this inevitably leading to the difference in the violation of E6 unification in the O and M worlds at lower energies: E6 → SO(10) × U(1)Z and E′6 → SU(6)′ × SU(2)′Z. Considering only asymptotically free theories, we present the evolution of all the inverse coupling constants αi−1(µ) in the one-loop approximation. In dealing with the M world involving MP violation, we then arrive at the model of the accelerating expansion of our Universe, where the axion (“acceleron”) belongs to the SU(2)′Z group of the M world. The coupling constant g′Z, which grows indefinitely at the scale Λ′Z ∼ 10−3 eV, is associated with this group. Within this theory, our Universe is in the false vacuum of the M world, in agreement with the phenomenologically observed cosmological constant of about (3 × 10−3 eV)4.