Searching for parity violation with the LIGO-Virgo-KAGRA network

A stochastic gravitational-wave background is expected to emerge from the superposition of numerous gravitational-wave sources of both astrophysical and cosmological origin. A number of cosmological models can have a parity violation, resulting in the generation of circularly polarized gravitational waves. We present a method to search for parity violation in the gravitational-wave data. We first apply this method to the most recent, third, LIGO-Virgo observing run. We then investigate the constraining power of future <math display="inline"><mrow><mi mathvariant="normal">A</mi><mo>+</mo><mi>LIGO</mi><mo>-</mo><mi>Virgo</mi></mrow></math> detectors, including KAGRA to the network, for a gravitational-wave background generated by early universe cosmological turbulence.