Generating enhanced parity-violating gravitational waves during inflation with violation of the null energy condition

A violation of the null energy condition (NEC) during inflation in a single-field inflation model will naturally enhance the amplitude of the parity violation effect (defined by $\Delta\chi$) of inflationary primordial gravitational waves (GWs), provided the inflaton is non-minimally coupled to a gravitational Chern-Simons term. After going through the NEC-violating phase, the Universe enters subsequent slow-roll inflation with a higher energy scale (i.e., a greater Hubble parameter $H$), which results in an enhanced nearly scale-invariant power spectrum (i.e., $P_{\rm T}$) of inflationary primordial GWs in the high-frequency band, while $P_{\rm T}$ remains consistent with observations in the frequency band of the cosmic microwave background. Therefore, the violation of NEC during inflation will amplify the observability (i.e., $P_{\rm T}\cdot\Delta\chi$) of the parity violation effect on small scales. Intriguingly, our model has particular oscillatory features on $\Delta\chi$ that may not be mimicked by others.