LAUSR

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 $H\ensuremath{\simeq}{H}_{inf1}$, the Universe goes through an NEC-violating period and then enters subsequent slow-roll inflation with a higher $H$ ($={H}_{inf2}\ensuremath{\gg}{H}_{inf1}$). The resulting primordial gravitational wave spectrum is nearly flat at the cosmic microwave background band, as well as at the frequency $f\ensuremath{\sim}1/\mathrm{yr}$ but with higher amplitude (compatible with the recent NANOGrav result). It is also highlighted that for the multistage inflation if the NEC violations happened intermittently, we might have a Great Wall--like spectrum of the stochastic GWB at the corresponding frequency band.