Relic backgrounds of gravitational waves from cosmic turbulence

Turbulence may have been produced in the early universe by several nonequilibrium processes. Periods of cosmic turbulence may have left a detectable relic under the form of stochastic backgrounds of gravitational waves. In this paper we derive general expressions for the power spectrum of the expected signal. Extending previous works on the subject, we take into account the effects of a continuous energy injection power and of magnetic fields. Both effects lead to relevant deviations from the Kolmogoroff turbulence spectrum. We apply our results to determine the spectrum of gravity waves which may have been produced by neutrino inhomogeneous diffusion and during a first order phase transition. We show that in both cases the expected signal may be in the sensitivity range of the interferometer LISA.