  Future gravitational wave observations are potentially sensitive to new
physics corrections to the Higgs potential once the first-order electroweak
phase transition arises. We study the SMEFT dimension-six operator effects on
the Higgs potential, where three types of effects are taken into account: (i)
SMEFT tree level effect on $\varphi^6$ operator, (ii) SMEFT tree level effect
on the wave function renormalization of the Higgs field, and (iii) SMEFT
top-quark one-loop level effect. The sensitivity of future gravitational wave
observations to these effects is numerically calculated by performing a Fisher
matrix analysis. We find that the future gravitational wave observations can be
sensitive to (ii) and (iii) once the first-order electroweak phase transition
arises from (i). The dimension-eight $\varphi^8$ operator effects on the
first-order electroweak phase transition are also discussed. The sensitivities
of the future gravitational wave observations are also compared with those of
future collider experiments.
