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