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.
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.
Quantum Information Dynamics of QED2 in Expanding de Sitter Universe
We study QED2 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 g2a(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 QED2 as a controlled setting for linking curved-space gauge dynamics, near-critical spectral structure, and operational irreversibility.
We study pseudo entropy S, a recent generalization of entanglement entropy, for scalar cosmological perturbations in de Sitter space with sound speed 0.024≤cs≤1, and in expanding and contracting FLRW backgrounds with varying equation-of-state parameter w. In de Sitter space, Re(S) grows after horizon exit while cs 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) 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), as well, which can encode the relative phase. 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 times that of Nielsen complexity. Unlike circuit complexity, whose saturation bound is w-independent, pseudo entropy is sensitive to w 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
A new dynamical paradigm merging quantum dynamics with cosmology is discussed. We distinguish between a universe and its background space-time. The universe here is the subset of space-time defined by Ψτ(x)≠0, where Ψτ(x) is a solution of a Schrödinger equation, x is a point in n-dimensional Minkowski space, and τ≥0 is a dimensionless ‘cosmic-time’ evolution parameter. We derive the form of the Schrödinger equation and show that an empty universe is described by a Ψτ(x) that propagates towards the future inside some future-cone V+. The resulting dynamical semigroup is unitary, i.e., ∫V+d4x|Ψτ(x)|2=1 for τ≥0. The initial condition Ψ0(x) is not localized at x=0. Rather, it satisfies the boundary condition Ψ0(x)=0 for x∉V+. For n=1+3 the support of Ψτ(x) is bounded from the past by the ‘gap hyperboloid’ ℓ2τ=c2t2−x2, where ℓ is a fundamental length. Consequently, the points located between the hyperboloid and the light cone c2t2−x2=0 satisfy Ψτ(x)=0, and thus do not belong to the universe. As τ grows, the gap between the support of Ψτ(x) and the light cone increases. The past thus literally disappears. Unitarity of the dynamical semigroup implies that the universe becomes localized in a finite-thickness future-neighbourhood of ℓ2τ=c2t2−x2, simultaneously spreading along the hyperboloid. Effectively, for large τ the subset occupied by the universe resembles a part of the gap hyperboloid itself, but its thickness Δτ is non-zero for finite τ. Finite Δτ implies that the three-dimensional volume of the universe is finite as well. An approximate radius of the universe, rτ, grows with τ due to Δτrτ3=Δ0r03 and Δτ→0. The propagation of Ψτ(x) through space-time matches an intuitive picture of the passage of time. What we regard as the Minkowski-space classical time can be identified with ctτ=∫d4xx0|Ψτ(x)|2, so tτ grows with τ as a consequence of the Ehrenfest theorem, and its present uncertainty can be identified with the Planck time. Assuming that at present values of τ (corresponding to 13–14 billion years) Δτ and rτ are of the order of the Planck length and the Hubble radius, we estimate that the analogous thickness Δ0 of the support of Ψ0(x) is of the order of 1 AU, and r03∼(ctH)3×10−44. The estimates imply that the initial volume of the universe was finite and its uncertainty in time was several minutes. Next, we generalize the formalism in a way that incorporates interactions with matter. We are guided by the correspondence principle with quantum mechanics, which should be asymptotically reconstructed for the present values of τ. We argue that Hamiltonians corresponding to the present values of τ approximately describe quantum mechanics in a conformally Minkowskian space-time. The conformal factor is directly related to |Ψτ(x)|2. As a by-product of the construction, we arrive at a new formulation of conformal invariance of m≠0 fields.
A bstract Understanding real-time dynamics of interacting quantum fields in curved space-time remains a major theoretical challenge. We employ tensor network methods to study such dynamics using interacting scalar and gauge theories in 1+1 spacetime dimensions, subject to a quench modeling a homogeneously expanding gravitational background. The models considered are the scalar λϕ 4 theory and the Schwinger model, i.e. a Dirac fermion coupled to a U(1) gauge field which is equivalent via bosonization to a scalar field with a cosine self-interaction. In the free scalar limit, both theories reproduce known analytical results, providing a nontrivial numerical validation of bosonization in curved spacetime for the Schwinger model. Our central finding is that self-interactions lead to a suppression of gravitational particle production compared to the free-field case, as evidenced by two-point functions and the spectra of produced particles. We further examine the behavior of entanglement generation and find that interactions suppress entanglement growth in the λϕ 4 theory, while in the Schwinger model, the interplay between suppressed particle production and enhanced inter-particle correlations leads to more complex entanglement behavior. Our results pave the way for further explorations of nonperturbative quantum real-time dynamics of interacting scalar and gauge theories in arbitrary gravitational backgrounds.
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.