Quantum Fluctuations, Decoherence of the Mean Field, and Structure Formation in the Early Universe

TL;DR

This paper investigates how quantum fluctuations in the early universe decohere into classical perturbations, showing that proper treatment of this transition aligns predictions with observations without fine-tuning parameters.

Contribution

It introduces a dynamical decoherence model for quantum fields in inflation, avoiding ad hoc assumptions and resolving issues with parameter fine-tuning in structure formation.

Findings

Proper quantum-to-classical transition predicts acceptable density contrast amplitudes.

Dynamical decoherence occurs through the field's own quantum fluctuations.

Eliminates need for unnaturally small coupling constants in inflation models.

Abstract

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 `dynamical decoherence' where an effective open quantum system decoheres through its own dynamics. The model we use to discuss fluctuation generation has the inflation field coupled to the graviton field. We show that when the quantum to classical transition is properly 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 inflation field ($\lambda$). The conventional treatment which requires an unnaturally small $\lambda \approx 10^{-12}$ stems from a basic flaw in naively identifying classical perturbations with quantum fluctuations.