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arXiv:2512.10126

Inflation is Not Magic

S. Shajidul Haque, Ghadir Jafari, Bret Underwood

hep-thgr-qcquant-phSubmitted Dec 10, 2025• Announced Dec 12, 2025• 0 citations
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Abstract

Cosmological perturbations generated during inflation exhibit striking quantum features, including entanglement and high circuit complexity. Yet their observational signatures remain effectively indistinguishable from classical stochastic variables. We quantify this tension by showing that quantum inflationary perturbations are continuous variable stabilizer states with vanishing quantum magic, a necessary resource for universal quantum computation as measured by Wigner negativity. Consequently, despite their quantum origins and description, these states can be efficiently simulated using classical algorithms. We further show that the Wigner negativity arising from primordial non-Gaussianity is suppressed not only by the non-linearity parameter $f_{NL}$, but also by the exponential squeezing of the perturbations. Viewing the early universe as a "high complexity, low magic" regime provides another perspective of what it means for the origin of structure in the universe to be "quantum."

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17 pages, 1 figure

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After a brief summary of the four main veins in the treatment of decoherence and quantum to classical transition in cosmology since the 1980s, we focus on one of these veins in the study of quantum decoherence of cosmological perturbations in inflationary universe, the case when it does not rely on any environment. This is what ‘intrinsic’ in the title refers to—a closed quantum system, consisting of a quantum field which drives inflation. The question is whether its quantum perturbations, which interact with the density contrast giving rise to structures in the universe, decohere with an inflationary expansion of the universe. A dominant view which had propagated for a quarter of a century asserts yes, based on the belief that the large squeezing of a quantum state after a duration of inflation renders the system effectively classical. This paper debunks this view by identifying the technical fault-lines in its derivations and revealing the pitfalls in its arguments which drew earlier authors to this wrong conclusion. We use a few simple quantum mechanical models to expound where the fallacy originated: The highly squeezed ellipse quadrature in phase space cannot be simplified to a line, and the Wigner function cannot be replaced by a delta function. These measures amount to taking only the leading order in the relevant parameters in seeking the semiclassical limit and ignoring the subdominant contributions where quantum features reside. Doing so violates the bounds of the Wigner function, and its wave functions possess negative eigenvalues. Moreover, the Robertson-Schrödinger uncertainty relation for a pure state is violated. For inflationary cosmological perturbations, in addition to these features, entanglement exists between the created pairs. This uniquely quantum feature cannot be easily argued away. Indeed, it could be our best hope to retroduce the quantum nature of cosmological perturbations and the trace of an inflation field. All this points to the invariant fact that a closed quantum system, even when highly squeezed, evolves unitarily without loss of coherence; quantum cosmological perturbations do not decohere by themselves.
Inflationary cosmology successfully accounts for the observed properties of primordial fluctuations using quantum field theory in an expanding background. However, the quantum nature of these fluctuations has not been experimentally established, since classical stochastic models could reproduce the observed two-point statistics by construction. Existing approaches to testing primordial quantumness focus primarily on Bell inequalities, which provide a sharp conceptual criterion but are difficult to implement with cosmological observables. In this work we adopt a falsification-based approach. We define a precise classical hypothesis for the origin of primordial perturbations (local stochastic fields admitting a positive probability distribution) and identify inequality constraints that must be satisfied within this class. We show how violations of these classicality inequalities can be probed using realistic cosmological observables, without invoking Bell tests or non-commuting measurement settings. We further identify symmetry-protected spectator sectors in which quantum coherence is parametrically preserved during inflation, allowing violations of observable magnitude to survive decoherence. Our results show that large-scale structure and future 21 cm surveys provide a viable and quantitative route to falsifying classical stochastic descriptions of primordial fluctuations.
A bstract Understanding how well future cosmological experiments can reconstruct the mechanism that generated primordial inhomogeneities is key to assessing the extent to which cosmology can inform fundamental physics. In this work, we apply a quantum metrology tool — the quantum Fisher information — to the squeezed quantum state describing cosmological perturbations at the end of inflation. This quantifies the ultimate precision achievable in parameter estimation, assuming ideal access to early-universe information. By comparing the quantum Fisher information to its classical counterpart — derived from measurements of the curvature perturbation power spectrum alone (homodyne measurement) — we evaluate how close current observations come to this quantum limit. Focusing on the tensor-to-scalar ratio as a case study, we find that the gap between classical and quantum Fisher information grows exponentially with the number of e -folds a mode spends outside the horizon. This suggests the existence of a highly efficient (but presently inaccessible) optimal measurement. Conversely, we show that accessing the decaying mode of inflationary perturbations is a necessary (but not sufficient) condition for exponentially improving the inference of the tensor-to-scalar ratio.
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 investigate the quantumness of primordial cosmological fluctuations and its detectability. The quantum discord of inflationary perturbations is calculated for an arbitrary splitting of the system, and shown to be very large on super-Hubble scales. This entails the presence of large quantum correlations, due to the entangled production of particles with opposite momentums during inflation. To determine how this is reflected at the observational level, we study whether quantum correlators can be reproduced by a nondiscordant state, i.e. a state with vanishing discord that contains classical correlations only. We demonstrate that this can be done for the power spectrum, the price to pay being twofold: first, large errors in other two-point correlation functions that cannot however be detected since they are hidden in the decaying mode; second, the presence of intrinsic non-Gaussianity, the detectability of which remains to be determined but which could possibly rule out a nondiscordant description of the cosmic microwave background. If one abandons the idea that perturbations should be modeled by quantum mechanics and wants to use a classical stochastic formalism instead, we show that any two-point correlators on super-Hubble scales can be exactly reproduced regardless of the squeezing of the system. The latter becomes important only for higher order correlation functions that can be accurately reproduced only in the strong squeezing regime.
In this work, we systematically investigate the quantum-information diagnostics of cosmological perturbations with a nontrivial sound speed, utilizing a normalized open two-mode squeezed-state framework. Rather than introducing new observables, our analysis focuses on how a modified sound speed dynamically reshapes the Schrödinger evolution of the squeezing parameters (rkr_krk​ and φkφ_kφk​). We demonstrate how these dynamical changes are inherited by the reduced density matrix of the observable sector. By employing a sound-speed-resonance parametrization, we derive and evaluate the purity, von Neumann entropy, Rényi entropies, and logarithmic negativity. To overcome the intrinsic multiscale stiffness of the post-inflationary equations, we introduce a bounded variable x=tanh⁡rkx = \tanh r_kx=tanhrk​ as a partial regularization, which enables reliable numerical simulations exclusively within the inflationary regime. Our numerical results reveal that a nontrivial sound speed significantly suppresses the purity of the reduced state, indicating enhanced effective mixedness. Simultaneously, it strongly amplifies and modulates both the entropic and entanglement diagnostics. More precisely, a nontrivial sound speed postpones the onset of classicality by modulating the decoherence process. Ultimately, we show that a nontrivial sound speed leaves distinct and identifiable quantum-information signatures within the entanglement structure of the early universe.