  The Hamiltonian approach to cosmological perturbations in general relativity
in finite space-time is developed, where a cosmological scale factor is
identified with spatial averaging the metric determinant logarithm.
  This identification preserves the number of variables and leads to a
cosmological perturbation theory with the scalar potential perturbations in
contrast to the kinetic perturbations in the Lifshitz version which are
responsible for the ``primordial power spectrum'' of CMB in the inflationary
model. The Hamiltonian approach enables to explain this ``spectrum'' in terms
of scale-invariant variables and to consider other topical problem of modern
cosmology in the context of quantum cosmological creation of both universes and
particles from the stable Bogoliubov vacuum.
