Gravitational waves from first-order cosmological phase transitions: lifetime of the sound wave source

We study particle-physics models for a first-order phase transition in the early universe, including models with polynomial potentials both with and without barriers at zero temperature, and Coleman-Weinberg-like models with potentials that are classically scale-invariant. We distinguish three possibilities for the transition - detonations, deflagrations and hybrids - and consider sound waves and turbulent mechanisms for generating gravitational waves during the transitions in these models. We argue that in models without a zero-temperature barrier and in scale-invariant models the period during which sound waves generate gravitational waves lasts only for a fraction of a Hubble time after a generic first-order cosmological phase transition, whereas it may last longer in some models with a zero-temperature barrier that feature severe supercooling. We illustrate the implications of these results for future gravitational-wave experiments.