Uncertainty relations for cosmological particle creation and existence
  of large fluctuations in reheating
  We derive an uncertainty relation for the energy density and pressure of a
quantum scalar field in a time-dependent, homogeneous and isotropic, classical
background, which implies the existence of large fluctuations comparable to
their vacuum expectation values. A similar uncertainty relation is known to
hold for the field square since the field can be viewed as a Gaussian random
variable. We discuss possible implications of these results for the reheating
process in scalar field driven inflationary models, where reheating is achieved
by the decay of the coherently oscillating inflaton field. Specifically we
argue that the evolution after backreaction can seriously be altered by the
existence of these fluctuations. For example, in one model the coherence of the
inflaton oscillations is found to be completely lost in a very short time after
backreaction starts. Therefore we argue that entering a smooth phase in thermal
equilibrium is questionable in such models and reheating might destroy the
smoothness attained by inflation.
