Effects of Lorentz symmetry breaking on quantum coherence in an expanding universe

This study investigates the interplay between Lorentz invariance violation (LIV) and quantum decoherence within an expanding universe. Motivated by quantum-gravity phenomenology, we incorporate a minimal length scale via spatial discretization, which leads to a modified dispersion relation of the form ω 2 = m 2 + k 2 − σ 2 k 4 , explicitly breaking Lorentz symmetry at high energies. When such LIV effects are coupled with cosmological expansion in a Friedmann-Robertson-Walker spacetime, they generate a distinct, cumulative decoherence signature. Using the l 1 -norm coherence measure, we quantify how the LIV parameter ( σ ) and the cosmological expansion parameters ( ξ, ρ ) jointly dictate the degradation of quantum coherence. Our analysis reveals a pronounced scale-dependent behavior: high-frequency modes ( k > 0.4) exhibit a resilience against decoherence, whereas low-frequency modes are markedly more susceptible. Furthermore, we identify specific parameter regimes where quantum coherence is maximized, indicating that certain cosmological conditions can mitigate the decoherence induced by fundamental symmetry breaking. This work establishes a concrete framework for connecting potential Planck-scale physics with observable quantum decoherence in cosmology, with broader implications for quantum information protocols in dynamical gravitational backgrounds.