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 x) of inflationary primordial gravitational waves (GWs), provided the inflaton is nonminimally 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., PT) of inflationary primordial GWs in the high-frequency band, while PT 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., PT center dot Delta x) of the parity -violation effect on small scales. Intriguingly, our model has particular oscillatory features on Delta x that may not be mimicked by others.