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We study the dependence of the observable stochastic gravitational wavebackground induced by a first-order phase transition on the global propertiesof the scalar effective potential in particle physics. The scalar potential canbe that of the Standard Model Higgs field, or more generally of any scalarfield responsible for a spontaneous symmetry breaking inbeyond-the-Standard-Model settings thatprovide for a first-order phasetransition in the early universe.Characteristics of the effective potentialinclude the relative depth of the true minimum ($E_\alpha^4$), the height ofthe barrier that separates it from the false one ($E_m^4$) and the separationbetween the two minima in field space ($v$), all at the bubble nucleationtemperature. We focus on a simple yet quite general class of single-fieldpolynomial potentials, with parameters being varied over several orders ofmagnitude. It is then shown that gravitational wave observatories such as aLIGOO5, BBO, DECIGO and LISA are mostly sensitive to values of these parameters inthe region $E_\alpha \sim (0.1-10) \times E_m$. Finally, relying onwell-defined models and using our framework, we demonstrate how to obtain thegravitational wave spectra for potentials of various shapes without necessarilyrelying on dedicated software packages.

Mapping the shape of the scalar potential with gravitational waves