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arXiv:2602.21263

Inflationary branch decoherence and the cosmological arrow of time

Ali Nayeri

gr-qcastro-ph.COhep-thquant-phSubmitted Feb 24, 2026• Announced Feb 25, 2026• Revised Jun 10, 2026 (v3)
v1 · Feb 24, 2026v2 · Mar 18, 2026v3 · Jun 10, 2026
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Abstract

We analyze branch decoherence in inflationary quantum cosmology by computing reduced density matrices and branch-overlap factors for long-wavelength perturbations. The Hartle-Hawking no-boundary state is real in the semiclassical regime and contains both expanding and contracting WKB components, whereas the tunneling state is selected as an outgoing complex WKB branch; expanding-contracting decoherence is therefore central for the former and mainly diagnostic for the latter. Using the influence-functional formalism, we derive the noise kernel for a light spectator environment and evaluate decoherence under horizon-based and EFT-motivated coarse grainings. We then compute the single-mode branch overlap directly from the Bunch-Davies mode functions, obtaining $|\mathcal{D}_k(z)|=[z^2/(z^2+1)]^{1/4}$ in the massless limit and $|\mathcal{D}_k(z)|\sim z^ν$ on superhorizon scales for massive fields, where $z=-kη$ is the dimensionless wavenumber with $η$ the conformal time. In the massless case, the accumulated geometric branch functional is evaluated in closed form, with a leading cutoff-sensitive phase-space term and a universal subleading contribution. The calculation provides an explicit quantitative bridge between quantum-cosmological boundary conditions, inflationary squeezing, and the emergence of effectively classical cosmological histories.

Journal reference
Phys. Rev. D 113, 126030 (2026)
DOI
10.1103/1k1w-c7vd
Comments
Accepted for publication in Physical Review D; 12 pages, 3 figures

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We analyze branch decoherence in inflationary quantum cosmology by computing reduced density matrices and branch-overlap factors for long-wavelength perturbations. The Hartle-Hawking no-boundary state is real in the semiclassical regime and contains both expanding and contracting WKB components, whereas the tunneling state is selected as an outgoing complex WKB branch; expanding-contracting decoherence is therefore central for the former and mainly diagnostic for the latter. Using the influence-functional formalism, we derive the noise kernel for a light spectator environment and evaluate decoherence under horizon-based and EFT-motivated coarse grainings. We then compute the single-mode branch overlap directly from the Bunch-Davies mode functions, obtaining ∣Dk(z)∣=[z2/(z2+1)]1/4|\mathcal{D}_k(z)|=[z^2/(z^2+1)]^{1/4}∣Dk​(z)∣=[z2/(z2+1)]1/4 in the massless limit and ∣Dk(z)∣∼zν|\mathcal{D}_k(z)|\sim z^ν∣Dk​(z)∣∼zν on superhorizon scales for massive fields, where z=−kηz=-kηz=−kη is the dimensionless wavenumber with ηηη the conformal time. In the massless case, the accumulated geometric branch functional is evaluated in closed form, with a leading cutoff-sensitive phase-space term and a universal subleading contribution. The calculation provides an explicit quantitative bridge between quantum-cosmological boundary conditions, inflationary squeezing, and the emergence of effectively classical cosmological histories.
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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
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This paper addresses a fundamental unresolved problem in inflationary cosmology: what quantum-state structure makes the one-realization classical description used in late-time cosmology physically meaningful within unitary quantum theory? We identify a structure that supports such a description, which we call Cosmological Classical Branches (CCBs). After reheating, the curvature perturbation is a collective variable rather than an independent subsystem. This shifts the classicality problem from the reduced state of the curvature perturbation itself to records of primordial information in the post-reheating matter state. When distinct matter components respond to the same primordial realization and their conditional states become distinguishable across different realizations, they carry records of the information about the curvature perturbation. A record in one component makes the realization readable, while a compatible record in a disjoint component suppresses interference accessible to operations confined to the first component, forming CCBs. Conditioning on a physical record yields a one-realization description within a CCB, in which the resolved primordial value acts as a c-number label while the matter degrees of freedom remain quantum. We test this criterion using effective models of two radiation fluids during radiation domination and of photons and cold dark matter around radiation--matter equality. We also show that a CCB typical with respect to the primordial Born measure exhibits the expected one-realization statistics: mode averages approach the primordial two-point statistics at fixed nonzero wavenumber in the large-volume limit. Overall, these results provide an operational framework at the quantum-state level connecting the primordial quantum superposition to the one-realization cosmological history assumed in standard cosmology.