  We study the observable implications of an incomplete first order phase
transition during inflation. In such a phase transition, the nucleated bubbles
do not percolate and instead are continuously produced until the onset of
reheating. The process creates an inhomogeneity with a distinct power spectrum
that depends on both the physics of the phase transition and the inflationary
dynamics. Upon horizon re-entry, this spectrum generates gravitational waves
through non-linear effects. This stochastic gravitational wave background is
predicted to have unique signatures that may be detectable by future
experiments spanning a wide frequency range. The discovery of such a
gravitational wave signal would shed a light on the detailed dynamics of
inflation.
