Generating enhanced parity-violating gravitational waves during inflation with violation of the null energy condition
Yong Cai
Abstract
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 $\mathrm{\ensuremath{\Delta}}\ensuremath{\chi}$) 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., ${P}_{\mathrm{T}}$) of inflationary primordial GWs in the high-frequency band, while ${P}_{\mathrm{T}}$ 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., ${P}_{\mathrm{T}}\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{\ensuremath{\Delta}}\ensuremath{\chi}$) of the parity-violation effect on small scales. Intriguingly, our model has particular oscillatory features on $\mathrm{\ensuremath{\Delta}}\ensuremath{\chi}$ that may not be mimicked by others.