Magnetic fields in a hot dense neutrino plasma and the gravitational waves

In the present work, we have studied the spectrum of the primordial gravitational waves due to magnetic instability in the presence of neutrino asymmetry. The magnetic instability generates a helical magnetic field on a large scale. The anisotropic stress generated by the magnetic field is shown to be a source of primordial gravitational waves at the time of matter-neutrino decoupling. We expect that the theoretically predicted gravitational waves by this mechanism may be detected by the Square Kilometer Array or pulsar time array observations. We also compare our findings with the results obtained by the earlier work where the effect of magnetic instability was not considered.