According to one formulation of the principle, energy and time can be related by the relation
In the modern view, energy is always conserved, but the eigenstates of the Hamiltonian (energy observable) aren't the same (don't commute) with the particle number operators.
Quantum fluctuations may have been very important in the origin of the structure of the universe: according to the model of inflation the ones that existed when inflation began were amplified and formed the seed of all current observed structure.