Towards Accurate Gravitational Wave Predictions: Gauge-Invariant Nucleation in the Electroweak Phase Transition

The vacuum decay in the early Universe should be gauge-invariant. In this work, we study the gauge dependence of the vacuum decay occurring through a first-order phase transition and the associated gravitational wave production. We investigate the gauge dependence of the bubble nucleation and phase transition parameters within the framework of the Standard model effective field theory in three dimension. By considering the power-counting and utilizing the Nielsen identity at finite temperature, we show that, depending on the power-counting scheme favored by the new physics scale, the perturbative computation methodology allow we get the gauge-independent nucleation rates and phase transition, this enables more accurate predictions of gravitational wave signatures.