Addressing the Gravitational Wave - Collider Inverse Problem

We provide a roadmap for analyzing the interplay between hypothetical future collider observations and the detection of a gravitational wave signal produced by a strong first order electroweak phase transition in beyond the Standard Model (BSM) theories. A cornerstone of this roadmap is a combination of a dimensionally reduced, three-dimensional effective field theory and results of both perturbation theory and non-perturbative lattice simulations. For the first time we apply these state-of-the-art methods to a comprehensive parameter space scan of a BSM theory. Concretely, we study an extension with the real scalar triplet, which admits a possible two-step electroweak symmetry-breaking thermal history. We find that (1) a first order transition during the second step could generate a signal accessible to LISA generation detectors and (2) the gravitational wave signal displays a strong sensitivity to the portal coupling between the new scalar and the Higgs boson, and (3) the ability for future experiments to detect the produced gravitational waves depends decisively on the wall velocity of the bubbles produced during the phase transition. We illustrate how a combination of direct and indirect measurements of the new scalar properties, in combination with the presence or absence of a gravitational wave detection, could test the model and identify the values of the model parameters.