The stochastic gravitational wave background (SGWB) produced at the electroweak phase transition is expected to be peaking within the sensitivity of the space-based GW detector LISA, 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 numerical simulations solving the highly non-linear 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 and pulsar timing array (PTA) observatories. I will focus on magnetically dominated MHD turbulence and compare to astrophysical and cosmological constraints that can provide a multi-messenger study of primordial magnetic fields. In particular, I will present the SGWB produced by decaying MHD turbulence, which has been validated by numerical simulations in a particular range of parameters. This model has been recently used to constrain the characteristics of a primordial magnetic field produced at the QCD phase transition by the recent evidence reported by the PTA collaborations.
This IFIC Seminar has received funding/support from the GVA Research Project "Understanding non-perturbative Phenomena in fundamental physics" (PROMETEO/2021/083)