Theoretical uncertainties for cosmological first-order phase transitions

We critically examine the magnitude of theoretical uncertainties in perturbative calculations of first-order phase transitions, using the Standard Model effective field theory as our guide. In the usual daisy-resummed approach, we find large uncertainties due to renormalisation scale dependence, which amount to two to three orders-of-magnitude uncertainty in the signal-to-noise ratio for gravitational wave experiments, such as LISA. Alternatively, utilising dimensional reduction in a more sophisticated perturbative approach drastically reduces this scale dependence. Further, this approach resolves other thorny problems with daisy resummation: it is gauge invariant which is explicitly demonstrated for the Standard Model, and avoids an uncontrolled derivative expansion in the bubble nucleation rate.