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arXiv:2604.02777

Quantum Information Dynamics of QED$_2$ in Expanding de Sitter Universe

Kazuki Ikeda, Yaron Oz

hep-thgr-qchep-latnucl-thquant-phSubmitted Apr 3, 2026• Announced Apr 6, 2026• 0 citations• Revised Jun 19, 2026 (v2)
v1 · Apr 3, 2026v2 · Jun 19, 2026
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Abstract

We study QED$_2$ in de Sitter space as a minimal interacting gauge theory in which cosmological expansion directly competes with quantum dynamics. In cosmic time, the hopping redshifts as $1/a(t)$ while the electric term grows as $g^2 a(t)$, sweeping the spectrum through a moving narrow-gap region in the $(τ,m)$ plane. Exact diagonalization shows that this defines a pseudo-critical line governing the loss of adiabaticity, excitation growth, and redshifted response. Using matrix-product states at a fixed mass, we separate the fixed-cutoff thermodynamic limit from the continuum extrapolation. The late-time dip survives in the infinite physical box size limit, and shifts to later $τ$ as the lattice spacing goes to zero, with current data favoring $τ_* \approx 3.1$, while the dip depth remains less controlled. For Gibbs initial states, the same mechanism produces an irreversibility front in the relative entropy that tracks the pseudo-critical line and is detectable via LOCC-accessible observables. These results identify de Sitter QED$_2$ as a controlled setting for linking curved-space gauge dynamics, near-critical spectral structure, and operational irreversibility.

Comments
24 pages, 3 figures

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Quantum Information Dynamics of QED2_22​ in Expanding de Sitter Universe
We study QED2_22​ in de Sitter space as a minimal interacting gauge theory in which cosmological expansion directly competes with quantum dynamics. In cosmic time, the hopping redshifts as 1/a(t)1/a(t)1/a(t) while the electric term grows as g2a(t)g^2 a(t)g2a(t), sweeping the spectrum through a moving narrow-gap region in the (τ,m)(τ,m)(τ,m) plane. Exact diagonalization shows that this defines a pseudo-critical line governing the loss of adiabaticity, excitation growth, and redshifted response. Using matrix-product states at a fixed mass, we separate the fixed-cutoff thermodynamic limit from the continuum extrapolation. The late-time dip survives in the infinite physical box size limit, and shifts to later τττ as the lattice spacing goes to zero, with current data favoring τ∗≈3.1τ_* \approx 3.1τ∗​≈3.1, while the dip depth remains less controlled. For Gibbs initial states, the same mechanism produces an irreversibility front in the relative entropy that tracks the pseudo-critical line and is detectable via LOCC-accessible observables. These results identify de Sitter QED2_22​ as a controlled setting for linking curved-space gauge dynamics, near-critical spectral structure, and operational irreversibility.
A bstract We study QED 2 in de Sitter space as a minimal interacting gauge theory in which cosmological expansion directly competes with quantum dynamics. In cosmic time, the hopping redshifts as 1/ a ( t ) while the electric term grows as g 2 a ( t ), sweeping the spectrum through a moving narrow-gap region in the ( τ , m ) plane. Exact diagonalization shows that this defines a pseudo-critical line governing the loss of adiabaticity, excitation growth, and redshifted response. Using matrix-product states at a fixed mass, we separate the fixed-cutoff thermodynamic limit from the continuum extrapolation. The late-time dip survives in the infinite physical box size limit, and shifts to later τ as the lattice spacing goes to zero, with current data favoring τ ∗ ≈ 3.1, while the dip depth remains less controlled. For Gibbs initial states, the same mechanism produces an irreversibility front in the relative entropy that tracks the pseudo-critical line and is detectable via LOCC-accessible observables. These results identify de Sitter QED 2 as a controlled setting for linking curved-space gauge dynamics, near-critical spectral structure, and operational irreversibility.
We study pseudo entropy S\mathcal{S}S, a recent generalization of entanglement entropy, for scalar cosmological perturbations in de Sitter space with sound speed 0.024≤cs≤10.024 \leq c_s \leq 10.024≤cs​≤1, and in expanding and contracting FLRW backgrounds with varying equation-of-state parameter www. In de Sitter space, Re(S)\mathrm{Re}(\mathcal{S})Re(S) grows after horizon exit while csc_scs​ controls its onset and saturates at late times. A similar saturation occurs in expanding-accelerating and contracting-decelerating backgrounds. In contrast, expanding-decelerating and contracting-accelerating backgrounds show large early-time Re(S)\mathrm{Re}(\mathcal{S})Re(S) followed by oscillations after horizon re-entry. This happens because while the squeezing freezes, the squeezing angle doesn't. Unlike entanglement entropy, pseudo entropy possesses an imaginary part, Im(S)\mathrm{Im}(\mathcal{S})Im(S), as well, which can encode the relative phase. Im(S)\mathrm{Im}(\mathcal{S})Im(S) decays to zero in de Sitter and expanding-accelerating cases, but forms dense sub-Hubble oscillation bands in expanding-decelerating and contracting-accelerating backgrounds. Compared with entanglement entropy, Krylov complexity, and Nielsen circuit complexity, pseudo entropy captures otherwise hidden phase information; in the unsaturated regime, its slope is 2\sqrt{2}2​ times that of Nielsen complexity. Unlike circuit complexity, whose saturation bound is www-independent, pseudo entropy is sensitive to www during the transition regime, making it a finer information theoretic diagnostic of cosmological dynamics.
Description: This theoretical study revisits the interpretation of cosmological end scenarios—such as heat death and asymptotic de Sitter expansion—through the framework of quantum decoherence and energy conservation in expanding spacetimes. Rather than treating late-time cosmology as an absolute termination of physical reality, the paper distinguishes between dynamical cessation and ontological nonexistence. Using explicit calculations of decoherence rates in FLRW backgrounds, we demonstrate that when environmental particle densities dilute as (a(t)^{-3}), the integrated decoherence over infinite future time can remain finite. Under such conditions, quantum superpositions formed beyond a critical cosmological time may never fully decohere. This does not imply recoherence, cyclic cosmology, or violation of thermodynamic irreversibility. Instead, it reflects the asymptotic disappearance of environmental interaction channels that dynamically sustain classical pointer states. The work therefore proposes that late-time cosmic evolution may be more coherently interpreted as a transition from environmentally enforced classicality to a regime of dominant quantum description. The analysis integrates principles from quantum field theory in curved spacetime, decoherence theory, and cosmological expansion dynamics, offering a conceptual clarification of what is meant by a “cosmic end.” 🔹 Keywords: Quantum cosmology; Quantum superposition; Decoherence; Early universe; Late universe; Environmental noise; Quantum–classical transition; Interaction density; Foundations of physics; Conceptual physics
Abstract Entanglement entropy (EE) of a spatial region quantifies correlations between the region and its surroundings. For a free scalar in the adiabatic vacuum in de Sitter space the EE is known to remain low, scaling as the surface area of the region. Here, we study the evolution of entanglement after the universe transitions from de Sitter to flat space. We concentrate on the case of a massless minimally coupled scalar. We find numerically that, after the de Sitter stage ends, the EE and the Ŕenyi entropy rapidly grow and saturate at values obeying the volume law. The final state of the subsystem (region) is a partially thermalized state reminiscent of a generalized Gibbs ensemble. We comment on application of our results to the question of when and how cosmological perturbations decohere.
We examine geometry and dynamics of classical spacetime derived from entanglement spectrum. The spacetime is a kind of canonical parameter space defined by the Fisher information metric. As a concrete example, we focus on the spectrum for free fermions in spatially one dimension. The spectrum has exponential family form like thermal probability distribution owing to mixed-state feature emerging from truncation of environmental degrees of freedom. In this case, the Fisher metric is given by the second derivative of the Hessian potential that can be identified with the entanglement entropy. We emphasize that the canonical parameters are nontrivial functions of partial system size by the truncation, filling fraction of fermions, and time. Then, the precise determination of this nontrivial mapping is necessary to derive the functional form of the Hessian potential that leads to correct entanglement entropy scaling. By this potential, we find that the emergent geometry becomes anti-de Sitter spacetime with imaginary time, and a radial axis as well as spacetime coordinates appears spontaneously. We also find that the information of the UV limit of the original free fermions lives in the boundary of the anti-de Sitter spacetime. These findings strongly suggest that the Hessian potential for free fermions has enough geometrical meaning associated with gauge-gravity correspondence. Furthermore, some deformation of the spectrum near the conformal fixed point is mapped onto spacetime dynamics. The fluctuation of the entanglement entropy embedded into the spacetime behaves like free scaler field, and the dynamics is described by the Einstein equation with a negative cosmological constant. Therefore, the Einstein equation can be regarded as the equation of original quantum state.
We study nonperturbative aspects of quantum field theory (QFT) in rigid anti de Sitter (AdS) spacetime using quantum information theoretic methods. While irreversibility of renormalization group (RG) flows is well established in flat space, it is not obvious whether it persists in AdS, where negative curvature and an asymptotic timelike boundary significantly modify infrared dynamics. Using strong subadditivity and AdS invariance, we derive an entropic second-order differential inequality for the difference between the vacuum entanglement entropy of a QFT and that of its ultraviolet fixed point, evaluated for spherical bulk regions. This inequality allows us to define RG charges that measure the relevant number of degrees of freedom, and we prove the irreversibility of the RG in 2, 3,2,\,3,2,3, and 444 spacetime dimensions. We further analyze free scalar and fermion theories in AdS, developing lattice formulations adapted to the geometry and computing entanglement entropies and RG charges. In AdS2_22​, we obtain analytic results for a massive Dirac fermion and compare them with numerical lattice calculations. These examples illustrate the general irreversibility theorem and clarify the distinction between conformal and massive theories in AdS.