Quantum origin of suppression for vacuum fluctuations of energy
  By example of a model with a spatially global scalar field, we show that the energy density of zero-point modes is exponentially suppressed by an average number of field quanta in a finite volume with respect to the energy density in the stationary state of minimal energy. We describe cosmological implications of mechanism. 
Ja.V. Balitsky, V.V. Kiselev
gr-qc hep-th