Gravitational waves from first order phase transitions during inflation

We study the production, spectrum, and detectability of gravitational waves in models of the early Universe where first order phase transitions occur during inflation. We consider all relevant sources. The self-consistency of the scenario strongly affects the features of the waves. The spectrum appears to be mainly sourced by collisions of bubble of the new phases, while plasma dynamics (turbulence) and the primordial gauge fields connected to the physics of the transitions are generally subdominant. The amplitude and frequency dependence of the spectrum for modes that exit the horizon during inflation are different from those of the waves produced by quantum vacuum oscillations of the metric or by first order phase transitions not occurring during inflation. A not too large number of slow (but still successful) phase transitions can leave detectable marks in the common microwave background radiation, but the signal weakens rapidly for faster transitions. When the number of phase transitions is instead large, the primordial gravitational waves can be observed both in the common microwave background radiation or with LISA (but in this case only marginally, for the slowest transitions) and especially with DECIGO. We also discuss the nucleosynthesis bound and the constraints it places on the parameters of the models.