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arXiv:2606.07663

A Landscape of Cosmological Decoherence

S. Shajidul Haque, Bret Underwood

Published Jun 3, 2026• 0 citations
arXivHTMLPDF

Abstract

Current observations constrain primordial perturbations to be adiabatic, approximately Gaussian, and nearly-scale invariant. However, a generic mixed state satisfying these constraints has additional unconstrained degrees of freedom, which can be parameterized by the purity of the state and its momentum variance. This allowable parameter space reveals a unified geometric landscape of mixed states, allowing us to map and relate distinct models of decoherence and their respective pointer bases. Within this landscape we show that decoherence models that "classicalize" -- in the sense of admitting a regular, positive-definite Glauber-Sudarshan $P$-function -- must actively inject momentum into the system, exceeding that of the vacuum. The enhanced momentum sources the decaying mode of the curvature perturbation, backreacting on the Newtonian potential and radiation-era geometry. While this mode decays away fast enough to preserve the temporal coherence of the CMB acoustic peaks, requiring the potential to remain within linear perturbation theory places a model-independent bound on the momentum variance generated by any model of decoherence. This bound is definitively violated by decohered thermal states with more than $14$ e-folds of inflation, while a strong dependence on the number of e-folds restricts amplitude-basis decoherence to fewer than roughly $64$ e-folds of inflation in order to stay in the linear regime. Altogether, we present a unifying framework for evaluating the quantum-to-classical transition of the early universe.

DOI
10.48550/arxiv.2606.07663

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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
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.
Substrate framework's energy-eigenstate decoherence formula γeff = (ΔE/MPc2)2 × νP [1] depends on the energy gap between superposed states, not on cosmological distance directly. But typical ΔE values for thermal modes, particle physics processes, and inflaton field fluctuations are functions of cosmic energy density, which evolves dramatically over cosmic history. This paper develops the cosmological evolution of substrate intrinsic decoherence across the principal epochs: • Planck era (t ~ 10−44 s): Substrate framework breaks down; γ formula not applicable. • Inflation era (ΔE ~ 1016 GeV): γ ~ 1037 Hz. Catastrophically fast decoherence drives primordial perturbation classicalization — providing the microscopic mechanism for the well-known but mechanistically unexplained quantum-to-classical transition of cosmological perturbations. • EW epoch (ΔE ~ 100 GeV): γ ~ 109 Hz. Coherence time τ ~ ns; particle physics processes decohere rapidly. • QCD epoch (ΔE ~ 100 MeV): γ ~ 103 Hz. τ ~ ms. • Nucleosynthesis (ΔE ~ MeV): γ ~ 0.1 Hz. τ ~ 10 s. • Recombination (ΔE ~ 0.3 eV): γ ~ 10−15 Hz. τ ~ 30 Myr, longer than the age of the universe at that time — the threshold at which the universe becomes capable of sustaining cosmologically long quantum coherence. • Present era (ΔE ~ kBTCMB ~ 0.2 meV): γ ~ 10−21 Hz. τ ~ 30 Gyr, longer than the current age of the universe. Coherent quantum systems can persist for cosmological timescales. • de Sitter future: Floor of γ set by dark energy; in the limit, decoherence approaches a constant minimum tied to the cosmological constant. Three principal results: (i) The decoherence rate has dropped by ~58 orders of magnitude over cosmic history, from γ ~ 1037 Hz at inflation to γ ~ 10−21 Hz today. The universe has become exponentially more capable of sustaining coherent quantum behavior as it has cooled. (ii) Coherent quantum behavior is a late-universe phenomenon. Modern quantum-mechanical experiments (atom interferometry, molecular interferometry, atomic clocks, B-meson oscillations) require a low-energy-density universe to operate. They could not have been performed in the radiation-dominated era because thermal energies were too high. (iii) Substrate framework provides a microscopic mechanism for primordial perturbation classicalization. Inflaton field quantum fluctuations decohered at γ ~ 1037 Hz during inflation, becoming classical perturbations that seeded the large-scale structure observed today. This resolves a long-standing puzzle in cosmology, where the quantum-to-classical transition is traditionally treated as a black box. Additionally, the cosmological floor on momentum uncertainty Δpmin ≥ ℏH(t)/c evolved from Δpmin ~ MPc at Planck era to Δpmin ~ 10−61 kg·m/s today — a quantum bound that has weakened by ~60 orders of magnitude. In the early universe, quantum uncertainty operated at vastly different scales than today. These results imply that the substrate framework's intrinsic decoherence sector is fundamentally a cosmological history sector: the framework's quantum-mechanical behavior changes character with cosmic epoch. Quantum coherence is not a universal property but rather a feature of low-energy-density universes. The framework's testable predictions in the modern era (thermal molecular interferometry, atomic clocks) are made possible by the universe having sufficiently cooled. Section II clarifies what does and doesn't depend on cosmic time. Section III develops the cosmological floor evolution. Section IV develops the decoherence rate across cosmic history with a master table. Section V addresses the early universe's rapid classicalization. Section VI addresses the inflation era specifically and primordial perturbations. Section VII addresses the present era. Section VIII addresses the de Sitter future. Section IX synthesizes the cross-epoch comparison of quantum properties. Section X concludes. Keywords: substrate theory; cosmological decoherence; primordial perturbations; inflation; quantum-to-classical transition; cosmological floor; energy-eigenstate formula; cosmic evolution of quantum capacity.
In this thesis, we study the decoherence of cosmological scalar perturbations during inflation. We first discuss the FRW model and cosmic inflation. Inflation is a period of accelerated expansion in the early universe, in typical models caused by a scalar field called inflaton. We review cosmological perturbation theory, where perturbations of the inflaton field and scalar degrees of freedom of the metric tensor are combined into the gauge-invariant Sasaki-Mukhanov variable. We quantize this variable using canonical quantization. Then, we discuss how interactions between the perturbations and their environment can lead to decoherence. In decoherence, the reduced density operator of the perturbations becomes diagonal with respect to a particular pointer basis. We argue that the pointer basis for the cosmological scalar perturbations consists of approximate eigenstates of the field value operator. Finally, we discuss how decoherence can help understand the transition from quantum theory to classical perturbation theory, and justify the standard treatment of perturbations and their initial conditions in cosmology. We conclude that since decoherence should not spoil the observationally successful predictions of this standard treatment, it is unlikely that the actual amount of decoherence could be observed in, say, the CMB radiation.
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
Inflation stretches quantum vacuum fluctuations into the density ripples we later see imprinted on the cosmic microwave background, yet the initial state is a pure, highly squeezed quantum state. The usual explanation for why those ripples look classical appeals to decoherence and the fading of a "decaying mode." This paper argues that the sharper statement is objectivity: the ripples become a fact for all observers, in the precise sense of quantum Darwinism, exactly when the growing perturbation is redundantly recorded across a vast environment of short-wavelength and gravitational-wave modes. The paper models a single super-horizon mode and its environment exactly. It proves that, once the mode crosses the horizon, its amplitude is recorded so redundantly that even a tiny fragment of the environment already fixes it, while the number of independent records grows without bound as the universe expands. Horizon crossing is therefore a Darwinism–encoding transition: an information measure rises from zero to one bit as the mode freezes. And the environment singles out one objective observable — the curvature amplitude — while its conjugate is only globally encoded, readable by no bounded fragment. The results are closed-form, and their exact algebraic cores are verified by proof-checking software. The record strength is not a free parameter: it is fixed by the mode's decoherence, computed from gravitational theory, and the leftover quantum coherence falls off exponentially with the redundancy. In short: the sky is classical not merely because it decohered, but because horizon crossing broadcast it — copying each primordial fluctuation until it became a fact for everyone.