Semi-Analytic Calculation of the Gravitational Wave Signal From the
  Electroweak Phase Transition for General Quartic Scalar Effective Potentials
  Upcoming gravitational wave (GW) detectors might detect a stochastic
background of GWs potentially arising from many possible sources, including
bubble collisions from a strongly first-order electroweak phase transition. We
investigate whether it is possible to connect, via a semi-analytical
approximation to the tunneling rate of scalar fields with quartic potentials,
the GW signal through detonations with the parameters entering the potential
that drives the electroweak phase transition. To this end, we consider a finite
temperature effective potential similar in form to the Higgs potential in the
Standard Model (SM). In the context of a semi-analytic approximation to the
three dimensional Euclidean action, we derive a general approximate form for
the tunneling temperature and the relevant GW parameters. We explore the GW
signal across the parameter space describing the potential which drives the
phase transition. We comment on the potential detectability of a GW signal with
future experiments, and physical relevance of the associated potential
parameters in the context of theories which have effective potentials similar
in form to that of the SM. In particular we consider singlet, triplet, higher
dimensional operators, and top-flavor extensions to the Higgs sector of the SM.
We find that the addition of a temperature independent cubic term in the
potential, arising from a gauge singlet for instance, can greatly enhance the
GW power. The other parameters have milder, but potentially noticeable,
effects.
