Resonant Dynamics of Gravitational Wave and Chiral Alfv'en wave in the Early Universe

In this work, we investigate the resonant interaction between stochastic gravitational waves (GWs) and chiral Alfvén waves in a magnetized chiral plasma in the early Universe. Starting from covariant chiral magnetohydrodynamics coupled to linearized gravity, we derive a closed system of equations for the coupled chiral-Alfvén velocity and magnetic-field perturbations. Both analytics and numerics show a parametric resonance at the sum frequency of the two CVE-split branches, with an instability band that widens as the GW strain grows. This CVE-to-Alfvén ratio is not a free parameter. In the early Universe, it is fixed by the Standard Model's relativistic degrees of freedom. Including the plasma's backreaction on the GW makes the energy exchange nonlinear, breaking the usual single-frequency Manley-Rowe picture. For a self-consistent choice of parameters, where backreaction is only a small correction, the unsuppressed resonance still drives the system to a finite-time blow-up within a few Hubble times. We then work out the resonant frequencies and growth rates involved, mapping out what current and future gravitational-wave detectors could observe.