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A Diagnostic Persistence Functional for Quantum Decoherence in Inflationary Perturbations

Ayoub Taoussi

Published Apr 2, 2026• 0 citations
Publisher

Abstract

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

DOI
10.5281/zenodo.19391359

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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
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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
This research introduces a novel quantitative framework for understanding one of the most fundamental questions in theoretical physics: How and when do quantum systems become classical? By developing a normalized Quantum Persistence Function (QPF) , we provide a continuous measure of residual quantum coherence in open systems interacting with their environment. The framework is rigorously derived from the spin-boson model—a paradigm for studying decoherence—and distinguishes between Markovian (memoryless) and non-Markovian environments based on spectral density structure (Keywords) Quantum decoherence Inflationary cosmology Open quantum systems Quantum–classical transition Primordial perturbations Cosmic Microwave Background Non-Gaussianity Spin-boson model Environmental entanglement Planck mission
Inflation is the standard scenario for the Early Universe providing a mechanism to explain the generation of primordial density perturbations from which all the structures we see in the universe formed by subsequent gravitational growth (like, e.g., anisotropies of the Cosmic Microwave Background, or the large-scale distribution of galaxies). The inflationary seeds for structure formation are traced back to quantum fluctuations of one or more (scalar) fields. However galaxies or cluster of galaxies do behave as classical objects. This entails the issue of understanding a quantum-to-classical transition in a cosmological framework. From this point of view inflation and cosmological observations can represent an interesting laboratory to explore some issues related to the quantum measurement problem. This issue has been long known, still it has been not explored in full details, and recently there has been a renowned interest in it. The thesis will consist in a first part of review of the most recent studies on the subject. It will then focus on some aspects of the problem, namely how the classical to quantum transition impacts on primordial gravitational waves which are a smoking gun of inflation, and whether and how such a transition can leave specific signatures in cosmological observables that go beyond the usual analyses (such as, e.g., non-Gaussianity of the cosmological perturbations from inflation).
Description: This work explores the conditions under which quantum superposition may emerge or persist at cosmological scales, challenging the common assumption that the early universe was the most favorable environment for quantum coherence. While the universe is widely believed to have originated from a quantum regime, the extreme interaction density, thermal noise, and intense field couplings of the early universe are argued to have caused rapid decoherence, effectively suppressing sustained quantum superposition beyond minimal scales. In this sense, the early universe is interpreted as a decoherence-dominated environment rather than a coherent quantum domain. The paper proposes an alternative perspective in which the late universe, characterized by cosmic expansion, reduced interaction density, and lower environmental noise, may offer more favorable conditions for partial isolation and the re-emergence of quantum superposition under specific circumstances. This conceptual framework reframes the quantum–classical transition as an environmentally driven process rather than a purely temporal or scale-dependent one, contributing to ongoing discussions in quantum cosmology, decoherence theory, and the foundations of physics. 🔹 Keywords: Quantum cosmology; Quantum superposition; Decoherence; Early universe; Late universe; Environmental noise; Quantum–classical transition; Interaction density; Foundations of physics; Conceptual physics