Mirror world and superstring-inspired hidden sector of the Universe, dark matter and dark energy

We develop a concept of parallel existence of the ordinary (O) and hidden (H) worlds. We compare two cases: (1) when the hidden sector of the Universe is a mirror counterpart of the ordinary world, and (2) when it is a superstring-inspired shadow world described, in contrast to the mirror world, by a symmetry group (or by a chain of groups), which does not coincide with the ordinary world symmetry group. We construct a cosmological model assuming the existence of the superstring-inspired E-6 unification, broken at the early stage of the Universe to SO(10) X U(1)(Z)-in the O-world, and to SU(6)' X SU(2)'(theta)-in the H-world. As a result, we obtain the low-energy symmetry group G'(SM) X SU(2)'(theta) in the shadow world, instead of the standard model group G(SM) existing in the O-world. The additional non-Abelian SU(2)'(theta) group with massless gauge fields, ''thetons,'' is responsible for dark energy. Considering a quintessence model of cosmology with an inflaton sigma and an axion a(theta), which is a pseudo Nambu-Goldstone boson induced by the SU(2)'(theta)-group anomaly, we explain the origin of dark energy, dark matter and ordinary matter. In the present model we review all cosmological epochs (inflation, reheating, recombination and nucleosynthesis), and give our version of the baryogenesis. The cosmological constant problem is also briefly discussed.