Quantum Entanglement Generation from Torsion-Induced Pseudoscalar Fragmentation: From Gradient Dynamics to Chiral Gravitational Waves

We demonstrate that spatial gradients of a torsion-induced pseudoscalar field T(x) act as a source of quantum entanglement in the early Universe. The field T(x) emerges from the totally antisymmetric component of the torsion tensor in Einstein Cartan gravity via Hodge duality, and possesses an approximate shift symmetry T →T+const, ensuring that only derivatives ∂µT enter physical observables. We show that the entanglement entropy production rate satisfies dS/dt ∝ ⟨(∇T)2⟩, with a linear coefficient determined by Floquet exponents of parametric resonance. Using Mathieu equation analysis and covariance matrix methods for Gaussian states [8,9], we obtain R2 = 0.969 for the linear scaling relation. The same gradient dy namics produce a parity-violating stochastic gravitational wave background with circular polarization Π(k) ∝ (α/Λgrav)(k/H) ⟨ ˙T2⟩/ωk, where the RMS fluctua tion ⟨ ˙T 2⟩ (not the vanishing mean ⟨ ˙T⟩) drives the helicity-dependent instabil ity through second-order averaging. Parametric resonance amplification during tachyonic fragmentation boosts the chiral asymmetry to observable levels: Π ∼ 10−4 − 10−2 in the LISA/LIGO frequency range, with the resonance peak k∗ ∼ µ (where µ is the tachyonic mass scale) falling within the detector sensitivity band after cosmological redshifting. This establishes a concrete bridge between spacetime torsion, quantum information dynamics, and observable cosmological signatures.