Supersymmetric phase transitions and gravitational waves at LISA

Gravitational waves generated during a first-order electroweak phase transition have a typical frequency which today falls just within the band of the planned space interferometer LISA. Contrary to what happens in the standard model, in its supersymmetric extensions, the electroweak phase transition may be strongly first order providing a mechanism for generating the observed baryon asymmetry in the universe. We show that during the same transition the production of gravitational waves can be rather sizeable. While the energy density in gravitational waves can reach at most h(0)(2)Omega (gw) similar or equal to 10(-16) in the minimal supersymmetric standard model, in the next-to-minimal supersymmetric model in some parameter range, h(0)(2)Omega (gw) can be as high as 4 x 10(-11). A stochastic background of gravitational waves of this intensity is within the reach of the planned sensitivity of LISA. Since in the standard model the background of gravitational waves is totally neglegible, its detection would also provide a rather unexpected experimental signal of supersymmetry and a tool to discriminate among supersymmetric models with different I-Eggs content.