Quasi-conformal models are an appealing scenario that can offer naturally a strongly supercooled phase transition and a period of thermal inflation in the early Universe. A crucial aspect for the viability of these models is how the Universe escapes from the supercooled state. One possibility is that thermal inflation phase ends by nucleation and percolation of true vacuum bubbles. This route is not, however, always efficient. In such case another escape mechanism, based on the growth of quantum fluctuations of the scalar field that eventually destabilize the false vacuum, becomes relevant. We study both of these cases in detail in a simple yet representative model. We determine the duration of the thermal inflation, the curvature power spectrum generated for the scales that exit horizon during the thermal inflation, and the stochastic gravitational wave background from the phase transition. We show that these gravitational waves provide an observable signal from the thermal inflation in almost the entire parameter space of interest. Furthermore, the shape of the gravitational wave spectrum can be used to ascertain how the Universe escaped from supercooling.
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