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We examine from first principles one of the basic assumptions of modernquantum theories of structure formation in the early universe, i.e., theconditions upon which fluctuations of a quantum field may transmute intoclassical stochastic perturbations, which grew into galaxies. Our earlier workshave discussed the quantum origin of noise in stochastic inflation and quantumfluctuations as measured by particle creation in semiclassical gravity. Here wefocus on decoherence and the relation of quantum and classical fluctuations.Instead of using the rather ad hoc splitting of a quantum field into long andshort wavelength parts, the latter providing the noise which decoheres theformer, we treat a nonlinear theory and examine the decoherence of a quantummean field by its own quantum fluctuations, or that of other fields itinteracts with. This is an example of `dynamical decoherence' where aneffective open quantum system decoheres through its own dynamics. The model weuse to discuss fluctuation generation has the inflation field coupled to thegraviton field. We show that when the quantum to classical transition isproperly treated, with due consideration of the relation of decoherence, noise,fluctuation and dissipation, the amplitude of density contrast predicted fallsin the acceptable range without requiring a fine tuning of the couplingconstant of the inflation field ($\lambda$). The conventional treatment whichrequires an unnaturally small $\lambda \approx 10^{-12}$ stems from a basicflaw in naively identifying classical perturbations with quantum fluctuations.Comment: 35 pages, latex, 0 figure

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