Quantum fluctuations, decoherence of the mean field, and structure formation in the early Universe

We examine from first principles one of the basic assumptions of modern quantum theories of structure formation in the early Universe, i.e., the conditions upon which fluctuations of a quantum field may transmute into classical stochastic perturbations, which grew into galaxies. Our earlier works have discussed the quantum origin of noise in stochastic inflation and quantum fluctuations as measured by particle creation in semiclassical gravity. Here we focus on decoherence and the relation of quantum and classical fluctuations. Instead of using the rather ad hoc splitting of a quantum field into long and short wavelength parts, the latter providing the noise which decoheres the former, we treat a nonlinear theory and examine the decoherence of a quantum mean field by its own quantum fluctuations, or that of other fields it interacts with. This is an example of how a quantum system can be viewed as effectively open and decoheres through its own dynamics. The model we use to discuss fluctuation generation has the inflaton field coupled to the graviton field. We show that when the quantum to classical transition is propertly treated, with due consideration of the relation of decoherence, noise, fluctuation, and dissipation, the amplitude of density contrast predicted falls in the acceptable range without requiring a fine-tuning of the coupling constant of the inflaton field. The conventional treatment which requires an unnaturally small λ≊${10}^{\mathrm{-}12}$ in a λ${\mathrm{\Phi }}^4$ inflaton field stems from a basic flaw in naively identifying classical perturbations with quantum fluctuations. © 1995 The American Physical Society.