The SGWB produced by MHD turbulence in the early universe

Abstract: The stochastic gravitational wave background (SGWB) produced at the electroweak phase transition is expected to be peaking around LISA's sensitivity peak frequency, being a promising test of high energy physics and beyond Standard Model extensions. The contribution of magnetohydrodynamic (MHD) turbulence to the cosmological SGWB is one of the least understood sources due to the necessity, in general, to perform large-scale numerical simulations solving the full system of MHD equations. In this talk, I will review recent numerical simulations that have addressed this issue and studied the potential detectability of the resulting SGWB and its polarization by space-based GW detectors like LISA. I will focus on magnetically dominated MHD turbulence and review additional constraints on primordial magnetic fields. Finally, I will present an analytical template that has been validated by numerical simulations under certain assumptions and that has been recently used to constrain the characteristics of a primordial magnetic field produced at the QCD phase transition with the recently common-spectrum process reported by the different pulsar timing array collaborations.