  We report on the first joint analysis of observational signatures from the
electroweak baryogenesis in both gravitational wave (GW) detectors and particle
colliders. With an effective extension of the Higgs sector in terms of the
dimension-6 operators, we derive a strong first-order phase transition in
associated with a sizable CP violation to realize a successful electroweak
baryogenesis. We calculate the GW spectrum resulting from the bubble
nucleation, plasma transportation, and magnetohydrodynamic turbulence of this
process that occurred after the big bang, and find that it yields GW signals
testable in Evolved Laser Interferometer Space Antenna, Deci-hertz
Interferometer Gravitational wave Observatory and Big Bang Observer. We further
identify collider signals from the same mechanism that are observable at the
planning Circular Electron Positron Collider. Our analysis bridges
astrophysics/cosmology with particle physics by providing significant
motivation for searches for GW event peaking at the $(10^{-4}, 1)$ Hz range,
which are associated with signals at colliders, and highlights the possibility
of an interdisciplinary observational window into baryogenesis. The technique
applied in analyzing early universe phase transitions may enlighten the study
of phase transitions in applied science.
