Gravitational radiation generated by cosmological phase transition magnetic fields

We study gravitational waves generated by the cosmological magnetic fields induced via bubble collisions during the electroweak (EW) and QCD phase transitions. The magnetic field generation mechanisms considered here are based on the use of the fundamental EW minimal supersymmetric and QCD Lagrangians. The gravitational waves spectrum is computed using a magnetohydrodynamic turbulence model. We find that the gravitational wave spectrum amplitude generated by the EW phase transition peaks at a frequency of approximately 1--2 mHz, and is of the order of ${10}^{\ensuremath{-}20}--{10}^{\ensuremath{-}21}$; thus this signal is possibly detectable by the Laser Interferometer Space Antenna (LISA). The gravitational waves generated during the QCD phase transition, however, are outside the LISA sensitivity bands.