  We investigate the parity-violating effects in primordial gravitational waves
(GWs) due to null energy condition (NEC) violation in two very early universe
scenarios: bounce-inflation and intermediate NEC violation during inflation. In
both scenarios, we numerically solve the power spectra of parity-violating
primordial GWs generated by coupling the background field and the spectator
field with the Nieh-Yan term, respectively. We find that the background field
can significantly enhance parity-violating effects at scales corresponding to
the maximum of the GW power spectra. In contrast, the parity-violating effects
produced by the spectator show significantly weaker observability even if the
coupling constant is large. Therefore, in NEC-violating scenarios, the
significant observable parity-violating effects in primordial GWs primarily
arise from the physics directly related to NEC violation. This result
highlights the potential of primordial GWs as crucial tools for exploring
NEC-violating and parity-violating physics.
