Title: BSMPT v3 A Tool for Phase Transitions and Primordial Gravitational Waves in Extended Higgs Sectors

Abstract: 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.