  Mirror world, a parallel hidden sector with microphysics identical to
ordinary particle physics, can have several interesting phenomenological and
astrophysical implications and mirror matter can be a natural candidate for
dark matter in the universe. In this thesis we analyze in detail some of its
implications in cosmology, in particular at the primordial nucleosynthesis
epoch. Big Bang Nucleosynthesis limits require that the temperature T' of the
mirror world should be at least twice lower than that of the ordinary world T.
We present numerical calculations regarding the nucleosynthesis epoch and
calculate the light and heavier element abundances in both ordinary and mirror
worlds as a function of x=T'/T. While the mirror world should be essentially
Helium dominated, we show that the heavier elements primordial abundances in
mirror world can be significantly higher than in the ordinary world. We also
study the cosmological bounds on the kinetic mixing between the photon and
mirror photon which in fact renders the mirror particles "millicharged" with
respect to the ordinary photon, with small electric charges proportional to the
photon kinetic mixing parameter. These bounds are important regarding the
possibility of mirror dark matter detection in the DAMA/Libra experiment. This
Diploma Thesis was defended in the University of L'Aquila in October 2007.
