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We have developed a concept of parallel existence of the ordinary (O) andmirror (M), or shadow (Sh) worlds. E_6 unification, inspired by superstringtheory, restores the broken mirror parity at the scale ~ 10^18 GeV. With theaim to explain the tiny cosmological constant, we consider the breakings: E_6-> SO(10) X U(1)_Z - in the O-world, and E'_6 -> SU(6)' X SU(2)'_\theta - inthe Sh-world. We assume the existence of shadow \theta-particles and the lowenergy symmetry group SU(3)'_C X SU(2)'_L X SU(2)'_\theta X U(1)'_Y in theshadow world, instead of the Standard Model. The additional non-AbelianSU(2)'_\theta group with massless gauge fields, "thetons", has a macroscopicconfinement radius 1/\Lambda'_\theta. The assumption that\Lambda'_\theta\approx 2.3 X 10^-3 eV explains the tiny cosmological constantgiven by recent astrophysical measurements. Searching for the Dark Matter (DM),it is possible to observe and study various signals of theta-particles.

Astrophysical Implications of the Superstring-Inspired E_6 Unification and Shadow Theta-Particles