  There can exist a parallel `mirror' world which has the same particle physics
as the observable world and couples the latter only gravitationally. The
nucleosynthesis bounds demand that the mirror sector should have a smaller
temperature than the ordinary one. By this reason its evolution should be
substantially deviated from the standard cosmology as far as the crucial epochs
like baryogenesis, nucleosynthesis etc. are concerned. Starting from an
inflationary scenario which could explain the different initial temperatures of
the two sectors, we study the time history of the early mirror universe. In
particular, we show that in the context of the GUT or electroweak baryogenesis
scenarios, the baryon asymmetry in the mirror world should be larger than in
the observable one and in fact the mirror baryons could provide the dominant
dark matter component of the universe. In addition, analyzing the
nucleosynthesis epoch, we show that the mirror helium abundance should be much
larger than that of ordinary helium. The implications of the mirror baryons
representing a kind of self-interacting dark matter for the large scale
structure formation, the CMB anysotropy, the galactic halo structures,
microlensing, etc. are briefly discussed.
