Hunting for quantum spikes

The quantum structures called quantum spikes, corresponding to known classical spikes are presented. The latter may occur in the evolution of the homogeneous sector of the Hamiltonian dynamics describing the Belinski-Khalatnikov-Lifshitz conjecture. The question if classical spikes may survive quantization is examined. The answer is in the affirmative. However, this is rather a subtle effect that needs further examination by making use of sophisticated analytical and numerical tools. The spikes seem to be of fundamental importance, both at classical and quantum levels, as they may serve as seeds of real structures in the universe.