Relic Backgrounds of Gravitational Waves from Cosmic Turbulence

TL;DR

This work develops a generalized framework for relic gravitational waves produced by cosmic turbulence, incorporating continuous energy injection and magnetohydrodynamic effects. It derives generalized turbulence spectra, connects them to the stochastic GW background, and analyzes how these spectra modify the GW signal across different turbulence regimes. The authors apply the framework to two early-universe scenarios: turbulence from neutrino inhomogeneous diffusion before neutrino decoupling and turbulence from a first-order electroweak phase transition, finding that magnetic fields can substantially boost the GW signal and potentially bring it within LISA’s reach. The results establish a link between turbulence properties, primordial magnetic fields, and the observable stochastic GW background, highlighting favorable conditions for detection and implications for early-universe physics.

Abstract

Turbulence may have been produced in the early universe during several kind of non-equilibrium processes. Periods of cosmic turbulence may have left a detectable relic in 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 considerable deviations from the Kolmogorov turbulence spectrum. We applied our results to determine the spectrum of gravity waves which may have been produced by neutrino inhomogeneous diffusion and by a first order phase transition. We show that in both cases the expected signal may be in the sensitivity range of LISA.

Figures (1)

• Figure 1: The figure shows whether an EWPT characterized by a pair $(\alpha,\beta)$ gives rise to a GW background from turbulence which is detectable by LISA. The shaded region is "detectable"; the dashed and continuous lines refer respectively to the Navier-Stokes and to the Magneto-Hydro-Dynamical case.