Exit from Inflation with a First-Order Phase Transition and a
  Gravitational Wave Blast
  In double-field inflation, which exploits two scalar fields, one of the
fields rolls slowly during inflation whereas the other field is trapped in a
meta-stable vacuum. The nucleation rate from the false vacuum to the true one
becomes substantial enough that triggers a first order phase transition and
ends inflation. We revisit the question of first order phase transition in an
"extended" model of hybrid inflation, realizing the double-field inflationary
scenario, and correctly identify the parameter space that leads to a first
order phase transition at the end of inflation. We compute the gravitational
wave profile which is generated during this first order phase transition.
Assuming instant reheating, the peak frequency falls in the $1$ GHz to $10$ GHz
frequency band and the amplitude varies in the range $10^{-11}\lesssim
\Omega_{\rm GW} h^2 \lesssim 10^{-8}$, depending on the value of the
cosmological constant in the false vacuum. The signature could be observed by
the planned Chongqing high frequency gravitational probe. For a narrow band of
vacuum energies, the first order phase transition can happen after the end of
inflation via the violation of slow-roll, with a peak frequency that varies
from $1$ THz to $100$ THz. For smaller values of cosmological constant, even
though inflation can end via slow-roll violation, the universe gets trapped in
a false vacuum whose energy drives a second phase of eternal inflation. This
range of vacuum energies do not lead to viable inflationary models, unless the
value of the cosmological constant is compatible with the observed value,
$M\sim 10^{-3}$ eV.
