Exotic Gravitational Wave Signatures from Simultaneous Phase Transitions

We demonstrate that the relic gravitational wave background from a multi-step phase transition may deviate from the simple sum of the single spectra, for phase transitions with similar nucleation temperatures $T_N$. We demonstrate that the temperature range $\Delta T$ between the volume fractions $f(T)=0.1$ and $f(T)=0.9$ occupied by the vacuum bubbles can span $\sim 20$ GeV. This allows for a situation in which phase transitions overlap, such that the later bubbles may nucleate both in high temperature and intermediate temperature phases. Such scenarios may lead to more exotic gravitational wave spectra, which cannot be fitted that of a consecutive PTs. We demonstrate this explicitly in the singlet extension of the Standard Model. Finally, we comment on potential additional effects due to the more exotic dynamics of overlapping phase transitions.