Intermittent null energy condition violations during inflation and primordial gravitational waves

Primordial null energy condition (NEC) violation would imprint a blue-tilted spectrum on gravitational wave background (GWB). However, its implications the GWB might be far richer than expected. We present scenario, in which after slow-roll (NEC-preserving) inflation with Hubble parameter $H\ensuremath{\simeq}{H}_{inf1}$, Universe goes through an NEC-violating period and then enters subsequent higher $H$ ($={H}_{inf2}\ensuremath{\gg}{H}_{inf1}$). The resulting primordial is nearly flat at cosmic microwave band, as well frequency $f\ensuremath{\sim}1/\mathrm{yr}$ but amplitude (compatible recent NANOGrav result). It also highlighted that for multistage if NEC violations happened intermittently, we have Great Wall--like of stochastic corresponding band.