  This is the first paper of a series devoted to the study of the cosmological
implications of the parallel mirror world with the same microphysics as the
ordinary one, but having smaller temperature, with a limit set by the BBN
constraints. The difference in temperature of the ordinary and mirror sectors
generates shifts in the key epochs for structure formation, which proceeds in
the mirror sector under different conditions. We consider adiabatic scalar
primordial perturbations as an input and analyze the trends of all the relevant
scales for structure formation (Jeans length and mass, Silk scale, horizon
scale) for both ordinary and mirror sectors, comparing them with the CDM case.
These scales are functions of the fundamental parameters of the theory (the
temperature of the mirror plasma and the amount of mirror baryonic matter), and
in particular they are influenced by the difference between the cosmological
key epochs in the two sectors. Then we used a numerical code to compute the
evolution in linear regime of density perturbations for all the components of a
Mirror Universe: ordinary baryons and photons, mirror baryons and photons, and
possibly cold dark matter. We analyzed the evolution of the perturbations for
different values of mirror temperature and baryonic density, and obtained that
for x=T'/T less than a typical value x_eq, for which the mirror baryon-photon
decoupling happens before the matter-radiation equality, mirror baryons are
equivalent to the CDM for the linear structure formation process. Indeed, the
smaller the value of x, the closer mirror dark matter resembles standard cold
dark matter during the linear regime.
