Unpolarized Low-Frequency Tail of Causal Chiral Gravitational Waves

Parity violation in the early Universe may lead to a chiral gravitational wave background. We show that, for finite-time parity-violating sources, the low-frequency tail of the generated chiral gravitational wave background is universally unpolarized, and that the chirality fraction decreases linearly with frequency. Our result generally applies to any parity-violating gravitational-wave source that appears quadratically in the wave equation. We consider both Gaussian sources and explicit trispectrum templates. We attribute the lack of chirality of the low-frequency tail to the fact that, on large scales, gravitational wave generation is almost equally inefficient for both helicities.