Temporal Field Fragmentation: A Universal Mechanism for Chiral Gravitational Wave Production

Fermionic loop corrections dynamically generate both the kinetic normalization and a periodic effective potential for the temporal scalar field T(x), rooted in the chiral anomaly and its gravitational extension. We demonstrate that this framework naturally gives rise to a controlled infrared tachyonic instability (m2 eff < 0) while strictly preserving gradient stability (c2 s > 0) within a consistent effective field theory. The instability amplifies long-wavelength modes exponentially until non linear backreaction sets in at ⟨δT2⟩ ∼ f2 T, leading to fragmentation of the field. The resulting anisotropic stress sources a stochastic gravitational wave background with a characteristic broken power-law spectrum. Remarkably, the peak amplitude ΩGWh2 ∼ 10−7 is universal and depends primarily on the thermal history (g∗) rather than microscopic scales, making it a robust prediction. The infrared scaling ΩGW ∝f3 follows from causality, rendering it model-independent. In the presence of a gravitational Chern–Simons coupling, the signal becomes strongly chiral, with frequency-dependent polarization degree ΠGW(f) = tanh(2πf∆T/fT), providing a distinctive observational signature accessible to future interferometers. These results establish temporal fragmentation as a predictive and testable mechanism for gravitational wave production in the early Universe.