Circular polarization of gravitational waves from early-Universe helical turbulence

We perform direct numerical simulations to compute the net circular polarization of gravitational waves from helical (chiral) turbulent sources in the early universe for a variety of initial conditions, including driven (stationary) and decaying turbulence. We investigate the resulting gravitational wave signal assuming different turbulence geneses such as magnetically or kinetically driven cases. Under realistic physical conditions in the early universe we compute numerically for the first time the total (integrated over all wavenumbers) polarization degree of the gravitational waves. We find that the spectral polarization degree strongly depends on the initial conditions. The peak of the spectral polarization degree occurs at twice the typical wavenumber of the source, as expected, and for fully helical decaying turbulence, it reaches its maximum (100%) only at the peak. We determine the temporal evolution of the turbulent sources as well as the resulting gravitational waves, showing that the dominant contribution to their spectral energy density happens shortly after the source activation. Only through an artificially prolonged decay of the turbulence can further increase of the gravitational wave amplitude be achieved. We estimate the detection prospects for the net polarization arguing that its detection contains clean information (including the generation mechanisms, time and strength) about the sources of possible parity violations in the early universe.