Gravitational Waves from Tachyonic Fragmentation of a Scalar Order Parameter

We investigate the generation of a stochastic gravitational wave background from the spinodal decomposition of a scalar order parameter τ(x) in the early Universe. In contrast to first-order phase transitions proceeding via bubble nucleation, the dynamics is driven by a tachyonic instability leading to exponential growth of long-wavelength modes followed by nonlinear fragmentation into localized field configurations. We present analytical estimates and 2D lattice simulations demonstrating that this process produces a distinct gravitational wave spectrum, characterized by a steep ultraviolet tail ΩGW ∝ k−n with n ≃ 3–5 (with our 2D simulation yielding n ≃ 5 as an upper bound, while 3D is expected to give n ≃ 3–4), reflecting the smoothness of the underlying field configurations. We derive the scaling of the peak amplitude Ωpeak GW,0h2 ∼ N2(m/MPl)2, where N encodes the duration of coherent anisotropic stress sourcing. This establishes spinodal fragmentation as a physically robust source of gravitational waves, providing a new observational window into non-equilibrium phase transitions beyond the standard paradigm.