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A Diagnostic Criterion for Decoherence Efficiency in Inflationary Perturbations

Ayoub Taoussi

Published Mar 5, 2026• 0 citations
Publisher

Abstract

This preprint develops a model-independent diagnostic framework for evaluating decoherence efficiency in inflationary curvature perturbations within an open quantum system formulation. The work does not introduce a new decoherence mechanism; instead, it constructs a normalized dimensionless functional intended to provide a systematic basis for comparing environmental decoherence scenarios in primordial cosmology. A persistence functional is derived to characterize the attenuation of off-diagonal density matrix components under inflationary expansion. Using a representative toy open-system model, the analysis demonstrates that the functional exhibits rapid suppression behavior associated with the exponential growth of comoving volume during inflation. The framework further suggests that residual quantum coherence may contribute to higher-order correlation functions of curvature perturbations. Accordingly, observational constraints on primordial non-Gaussianity may be interpreted as indirect lower bounds on decoherence efficiency. The formulation is intended as a diagnostic tool rather than a proposal of a new physical decoherence process. Keywords : Inflationary Cosmology Quantum Decoherence Primordial Perturbations Open Quantum Systems Classicality Non-Gaussianity

DOI
10.5281/zenodo.18876949

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This preprint develops a model-independent diagnostic framework for evaluating decoherence efficiency in inflationary curvature perturbations within an open quantum system formulation. The work does not introduce a new decoherence mechanism; instead, it constructs a normalized dimensionless functional intended to provide a systematic basis for comparing environmental decoherence scenarios in primordial cosmology. A persistence functional is derived to characterize the attenuation of off-diagonal density matrix components under inflationary expansion. Using a representative toy open-system model, the analysis demonstrates that the functional exhibits rapid suppression behavior associated with the exponential growth of comoving volume during inflation. The framework further suggests that residual quantum coherence may contribute to higher-order correlation functions of curvature perturbations. Accordingly, observational constraints on primordial non-Gaussianity may be interpreted as indirect lower bounds on decoherence efficiency. The formulation is intended as a diagnostic tool rather than a proposal of a new physical decoherence process. Keywords : Inflationary Cosmology Quantum Decoherence Primordial Perturbations Open Quantum Systems Classicality Non-Gaussianity
Description : This work introduces a novel, model-independent diagnostic framework for quantifying quantum decoherence in primordial inflationary perturbations. The study addresses the fundamental problem of the quantum-to-classical transition in cosmology by defining a normalized persistence functional that captures the suppression of quantum coherence over time. Within an open quantum system approach, each perturbation mode is treated as an effective quantum degree of freedom interacting with an environment, leading to Gaussian suppression of off-diagonal density matrix elements. The proposed functional provides a direct and scalable measure of decoherence efficiency without relying on detailed microscopic modeling. A key feature of the framework is the introduction of a residual coherence parameter, which accounts for possible late-time deviations from complete classicalization. The work further establishes a monotonicity property for the decoherence functional and connects the persistence measure to entropy growth, offering an information-theoretic interpretation of the decoherence process. Importantly, the framework suggests a phenomenological link between residual coherence and observable non-Gaussianity in the cosmic microwave background, opening a pathway for potential observational constraints. The proposed diagnostic functional is broadly applicable across inflationary models and provides a unified tool for comparing decoherence efficiency under different environmental interactions. This work lays the foundation for future studies on quantum signatures in cosmological observables and the persistence of quantum features in the early universe. Keywords : Quantum Decoherence Inflationary Cosmology Primordial Perturbations Open Quantum Systems Quantum-to-Classical Transition Non-Gaussianity Cosmological Perturbation Theory Density Matrix Quantum Cosmology Early Universe Physics Decoherence Functional Entropy and Information Theory
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Description This work proposes an information-theoretic framework for describing the quantum–classical transition during cosmological inflation through open quantum system dynamics and entanglement evolution. The study introduces a normalized Quantum Persistence Function (QPF) as a scale-invariant diagnostic measure of residual quantum coherence, formulated in representation-independent form using reduced density matrix purity and entropy growth. The framework connects microscopic decoherence processes with macroscopic cosmological observables by applying spin–boson open-system dynamics to inflationary perturbations. Classical emergence is interpreted as a dynamical suppression of quantum coherence driven by entanglement entropy growth between cosmological modes rather than by simple interference cancellation. Observational constraints from primordial Gaussianity bounds are used to derive an efficiency condition for decoherence during reheating, expressed as a lower bound on the decoherence functional. The results show that classicalization occurs well below holographic entropy saturation limits, suggesting that cosmological classical emergence is governed primarily by dynamical information redistribution rather than fundamental information capacity thresholds. This work is deposited on Zenodo as an open scientific preprint to encourage constructive discussion and feedback from the scientific community. KEYWORDS: Quantum classical transition; decoherence theory; inflationary cosmology; open quantum systems; entanglement entropy; cosmological perturbations; quantum persistence function; information theory in physics; primordial fluctuations; classical emergence dynamics
We study, within a toy model, how a thermal bath of cosmological perturbations can decohere the minisuperspace degrees of freedom of the universe, treating the perturbations as an environment in the framework of open quantum systems. Instead of tracing out the perturbations from a semiclassical ansatz for the total wave function, as in earlier approaches, we incorporate their backreaction on the background through an effective second-order coupling and derive a master equation. The model describes a spatially flat semiclassical universe during slow-roll inflation with a dust clock field, while scalar cosmological perturbations in a phenomenologically assumed thermal state constitute the environment. The master equation is non-Markovian, since the bath correlation functions do not decay in time. Within this framework, we find that, for a representative set of parameter estimates, the characteristic decoherence timescale corresponding to the thermal contribution can be shorter than the Hubble timescale. In addition, we address the question of whether the pointer-state structure induced by the decoherence in such a framework could provide a criterion for the choice of semiclassical states in quantum cosmology.