Gravitational wave spectra from strongly supercooled phase transitions

We study gravitational wave (GW) production in strongly supercooled cosmological phase transitions, taking particular care of models featuring a complex scalar field with a U(1) symmetric potential. We perform lattice simulations of two-bubble collisions to properly model the scalar field gradients, and compute the GW spectrum sourced by them using the thin-wall approximation in many-bubble simulations. We find that in the U(1) symmetric case the low-frequency spectrum is $$\propto \omega $$ whereas for a real scalar field it is $$\propto \omega ^3$$ . In both cases the spectrum decays as $$\omega ^{-2}$$ at high frequencies.