In de Sitter QED₂, expansion sweeps the spectrum across a pseudo-critical line that controls adiabaticity loss, excitation growth, and a late-time dip near τ_* ≈ 3.1.

Summary. The manuscript studies QED₂ in de Sitter as a minimal interacting gauge theory in which cosmological expansion 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 is used to identify a pseudo-critical line that governs loss of adiabaticity, excitation growth, and redshifted response. Matrix-product-state simulations at fixed mass are then used to separate the fixed-cutoff thermodynamic limit from the continuum extrapolation: the late-time dip is reported to survive the infinite physical box, to shift later as lattice spacing vanishes, and to favor τ_*≈3.1 (with dip depth less controlled). For Gibbs initial states the same mechanism produces an irreversibility front in relative entropy that tracks the pseudo-critical line and is claimed to be LOCC-detectable.

Significance. If the continuum and infinite-volume claims hold, the work supplies a controlled lattice setting that links curved-space gauge dynamics, near-critical spectral structure, and operational irreversibility. Explicit separation of the fixed-cutoff thermodynamic limit from continuum extrapolation, the use of both ED and MPS, and the LOCC-accessible relative-entropy diagnostic are genuine methodological strengths. A robust, continuum-controlled value of τ_* and a cleanly tracked irreversibility front would be of interest to both lattice gauge theory and quantum-information approaches to cosmology.