  Strong first-order phase transitions (SFOPT) during the evolution of the
Higgs potential in the early universe not only allow for the dynamical
generation of the observed matter-antimatter asymmetry, they can also source a
stochastic gravitational wave (GW) background possibly detectable with future
space-based gravitational waves interferometers. As SFOPTs are
phenomenologically incompatible with the Standard Model (SM) Higgs sector, the
observation of GWs from SFOPTs provides an exciting interplay between cosmology
and particle physics in the search for new physics. With the C++ code BSMPTv3,
we present for the first time a tool that performs the whole chain from the
particle physics model to the gravitational wave spectrum. Extending the
previous versions BSMPTv1 and v2, it traces the phases of beyond-SM (BSM) Higgs
potentials and is capable of treating multiple vacuum directions and multi-step
phase transitions. During the tracing, it checks for discrete symmetries, flat
directions, and electroweak symmetry restoration, and finally reports the
transition history. The transition probability from the false to the true
vacuum is obtained from the solution of the bounce equation which allows for
the calculation of the nucleation, percolation and completion temperatures. The
peak amplitude and frequency of the GWs originating from sound waves and
turbulence, are evaluated after the calculation of the thermal parameters at
the transition temperature, and finally the signal-to-noise ratio at LISA is
provided. The code BSMPTv3 is a powerful self-contained tool that comes more
than timely and will be of great benefit for investigations of the vacuum
structure of the early universe of not only simple but also complicated Higgs
potentials involving several vacuum directions, with exciting applications in
the search for new physics.
