Gravitational Radiation From Cosmological Turbulence

TL;DR

The paper develops a physics-based framework for the stochastic gravitational-wave background produced by cosmological turbulence during a first-order phase transition. It models the turbulent plasma with isotropic Kolmogorov scaling and computes the gravitational radiation from the turbulent motions, and separately from turbulence-generated magnetic fields, deriving relic spectra and energy densities. It compares the turbulence- and magnetic-field-induced backgrounds to the gravitational waves from bubble-wall collisions and assesses the prospects for detection by LISA and LIGO, concluding that turbulence at electroweak scales is unlikely to be detected with planned instruments, while bubble collisions remain more favorable. The results are formulated in a generic way that applies to any cosmological turbulence with an inertial range between L_S and L_D, and provide explicit expressions for h_c and Ω_GW as functions of phase-transition parameters.

Abstract

An injection of energy into the early Universe on a given characteristic length scale will result in turbulent motions of the primordial plasma. We calculate the stochastic background of gravitational radiation arising from a period of cosmological turbulence, using a simple model of isotropic Kolmogoroff turbulence produced in a cosmological phase transition. We also derive the gravitational radiation generated by magnetic fields arising from a dynamo operating during the period of turbulence. The resulting gravitational radiation background has a maximum amplitude comparable to the radiation background from the collision of bubbles in a first-order phase transition, but at a lower frequency, while the radiation from the induced magnetic fields is always subdominant to that from the turbulence itself. We briefly discuss the detectability of such a signal.