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 g² 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 QED₂ as a controlled setting for linking curved-space gauge dynamics, near-critical spectral structure, and operational irreversibility.