  A heuristic hypothesis about domination of Bose-Einstein statistics in the
early Universe is suggested. The possibility of Bose-Einstein condensation
(BEC) of primordial baryon-antibaryon pairs is considered. In accordance with
this postulation enormous masses in the order of galactic mass may be
accumulated within the cosmic scales. At the certain threshold value of the
matter density the structural bosons decay into fermions and the sharp
breakdown of quantum-mechanical symmetry of the particles wave functions
occurs. Then, due to the Pauli principle of exclusion a large-scale phase
transition occurs because of enormous pressure jump of the matter. This
phenomenon might cause Cosmological Bang at the beginning stage of the Matter
Era. As a mechanism of accumulation of galactic mass much larger than the
configuration with structural bosons, a hypothetical BEC of elementary bosons
(gauge bosons $W^{\pm}$ and $Z^{0})$ is discussed as well.
