Di-Higgs Production in the $4b$ Channel and Gravitational Wave
  Complementarity
  We present a complementarity study of gravitational waves and double Higgs
production in the $4b$ channel, exploring the gauge singlet scalar extension of
the SM. This new physics extension serves as a simplified benchmark model that
realizes a strongly first-order electroweak phase transition necessary to
generate the observed baryon asymmetry in the universe. In calculating the
signal-to-noise ratio of the gravitational waves, we incorporate the effect of
the recently discovered significant suppression of the gravitational wave
signals from sound waves for strong phase transitions, make sure that
supercooled phase transitions do complete and adopt a bubble wall velocity that
is consistent with a successful electroweak baryogenesis by solving the
velocity profiles of the plasma. The high-luminosity LHC sensitivity to the
singlet scalar extension of the SM is estimated using a shape-based analysis of
the invariant $4b$ mass distribution. We find that while the region of
parameter space giving detectable gravitational waves is shrunk due to the new
gravitational wave simulations, the qualitative complementary role of
gravitational waves and collider searches remain unchanged.
