Quantum decoherence in axion models of inflation

Cosmic inflation predicts the production of quantum fluctuations that seed all the structures present in the universe today. However, these structures (such as Cosmic Microwave Background anisotropies or the large-scale distribution of galaxies) are classical objects and show no sign of quantumness. The problem of quantum-to-classical transition arises - how did fluctuations, initially quantum in nature, become classical? Quantum decoherence is considered the leading mechanism of classicalization of the primordial perturbations. In the framework of decoherence, the primordial perturbations are viewed as an open quantum system interacting with a surrounding environment. The Lindblad equation can model the evolution of these perturbations, which will lead to decoherence and possibly to corrections to cosmological observables, such as the power spectrum of inflationary perturbations. This mechanism has been extensively studied in the recent literature in the context of single scalar field-driven inflation. We apply the Lindblad formalism to the axion models of inflation that involve the coupling $\phi \tilde{F}^{\mu\nu }F_{\mu \nu }$ to some gauge fields. In our construction, these gauge fields become the environment that decoheres the inflaton perturbations. This process is modeled using the Lindblad equation, and we study how decoherence affects the power spectrum of primordial perturbations in axion models of inflation. We also calculate the rate of decoherence in the said model. Additionally, we calculate the quantum discord as a measure of quantumness and find that on observable scales, we get both high and negligibly small values of discord. We also motivate the need to complement the study of quantum discord with other measures of quantumness, such as the Bell inequality violation or state separability.