Measuring gravitational wave spectrum from electroweak phase transition and Higgs self-couplings

In this work, we demonstrate the complete process of using space-based gravitational wave detectors to measure properties of the stochastic gravitational wave background arising from a first-order electroweak phase transition. Based on frequency-domain simulations of the Taiji mission, including instrumental noise and astrophysical foregrounds, we perform parameter inference using both the Fisher information matrix and Bayesian Markov Chain Monte Carlo sampling. We show how the reconstructed spectrum constrains the macroscopic parameters of the phase transition, and further how these constraints map onto the underlying particle-physics parameters in a singlet-extended Standard Model. Our results demonstrate that the Higgs cubic and quartic self-couplings can be significantly constrained using gravitational wave observations, despite limitations arising from parameter degeneracy.