Gravitational Wave Spectrum from QCD-Triggered Temporal Fragmentation

We propose a novel mechanism for stochastic gravitational wave background generation, where a geometric temporal scalar field T(x) — interpreted as a torsion induced pseudoscalar (axion-like) degree of freedom — undergoes a tachyonic insta bility triggered by the QCD topological susceptibility χtop(T ). The QCD crossover acts as a critical point where the effective mass m2 eff → 0, driving the adiabaticity parameter η → ∞ and guaranteeing a non-perturbative sudden quench. The re sulting fragmentation generates anisotropic stress ΠTT ij ∼∂iδT∂jδT, sourcing grav itational waves. Crucially, we demonstrate that detectability by current Pulsar Timing Arrays does not rely on the non-linear fragmentation dynamics: the pre ceding stiff epoch (w = 1) imprints a blue-tilted spectrum (ΩGW ∝ f2) that crosses the NANOGrav 15-yr sensitivity threshold for fractional energy density α ≳ 0.3. The fragmentation process adds a characteristic peak at f∗ ∼ 10−9 Hz, provid ing a unique spectral morphology that distinguishes this model from cosmic string networks. This two-component signal offers a direct observational probe of the geometric sector of gravity and the dynamics of time itself in the early Universe.