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In the present paper we have developed a concept of parallel ordinary (O) andmirror (M) worlds. We have shown that in the case of a broken mirror parity(MP), the evolutions of fine structure constants in the O- and M-worlds are notidentical. It is assumed that E_6-unification inspired by superstring theoryrestores the broken MP at the scale \sim 10^{18} GeV, what unavoidably leads tothe different E_6-breakdowns at this scale: E_6 \to SO(10)\times U(1)_Z - inthe O-world, and E'_6 \to SU(6)'\times SU(2)'_Z - in the M-world. Consideringonly asymptotically free theories, we have presented the running of all theinverse gauge constants \alpha_i^{-1} in the one-loop approximation. Then a`quintessence' scenario is discussed for our model of accelerating universe.Such a scenario is related with an axion (`acceleron') of a new gauge groupSU(2)'_Z which has a coupling constant g_Z extremely growing at the scale\Lambda_Z\sim 10^{-3} eV.

Mirror World with Broken Mirror Parity, E(6) Unification and Cosmology