Cosmological constant in a model with superstring-inspired E6 unification and shadow θ-particles

We have developed the concept of parallel existence of the ordinary (O-) and mirror (M-), or shadow (Sh-) worlds. In the first part of the paper we consider a mirror world with broken mirror parity and the breaking E6→SU(3)3 in both worlds. We show that in this case the evolutions of coupling constants in the O- and M-worlds are not identical, having different parameters for similar evolutions. E6 unification, inspired by superstring theory, restores the broken mirror parity at the scale ∝1018 GeV. With the aim to explain the tiny cosmological constant, in the second part we consider the breakings: E6→SO(10) x U(1)Z in the O-world, and E'6→SU(6) ' x SU(2)'θ in the Sh-world. We assume the existence of shadow θ-particles and the low-energy symmetry group SU(3)'C x SU(2)'L x SU(2)'θ x U(1)'Y in the shadow world, instead of the Standard Model. The additional non-Abelian SU(2) 'θ group with massless gauge fields, ''thetons'', has a macroscopic confinement radius 1/ Λ'θ. The assumption that Λ'θ ∼2.3 .10-3 eV explains the tiny cosmological constant given by recent astrophysical measurements. In this way the present work opens the possibility to specify a grand unification group, such as E6, from cosmology. (orig.)