NANOGrav Signal from the End of Inflation and the LIGO Mass and Heavier
  Primordial Black Holes
  Releasing the 12.5-year pulsar timing array data, the North American
Nanohertz Observatory for Gravitational Waves (NANOGrav) has recently reported
the evidence for a stochastic common-spectrum which would herald the detection
of a stochastic gravitational wave background (SGWB) for the first time. We
investigate if the signal could be generated from the end of a $\sim 10$ MeV
but still phenomenologically viable double-field inflation when the field
configuration settles to its true vacuum. During the double-field inflation at
such scales, bubbles of true vacuum that can collapse to LIGO mass and heavier
primordial black holes form. We show that only when this process happens with a
first-order phase transition, the produced gravitational wave spectrum can
match with the NANOGrav acclaimed SGWB signal. We show that the produced
gravitational wave spectrum matches the NANOGrav SGWB signal only when this
process happens through a first-order phase transition. Using LATTICEEASY, we
also examine the previous observation in the literature that by lowering the
scale of preheating, despite the shift of the peak frequency of the
gravitational wave profile to smaller values, the amplitude of the SGWB could
be kept almost constant. We notice that this observation breaks down at the
preheating scale, $M\lesssim 10^{-14}~m_{{}_{\rm Pl}}$.
