The Spectrum of Gravitational Radiation from Primordial Turbulence

TL;DR

This paper develops a first-principles real-space calculation of the relic gravitational wave spectrum produced by primordial turbulence with a stationary Kolmogorov spectrum lasting a finite duration. By modeling the turbulence with a Kolmogorov energy cascade and Kraichnan type time correlations, and by bridging a localized-source to homogeneous finite-duration regime, the authors derive the GW spectrum in terms of turbulence parameters such as the stirring scale, duration, Mach number, and Reynolds number. They translate the spectrum to present-day observables, discuss the aeroacoustic limit, and derive asymptotic behavior across frequency regimes, concluding that electroweak-scale turbulence could be detectable by future space-based detectors for a range of parameters. The work provides a framework to connect high-energy phase transition physics to a stochastic gravitational wave background and highlights observational challenges and potential features that would aid discrimination from foregrounds.

Abstract

Energy injection into the early universe can induce turbulent motions of the primordial plasma, which in turn act as a source for gravitational radiation. Earlier work computed the amplitude and characteristic frequency of the relic gravitational wave background, as a function of the total energy injected and the stirring scale of the turbulence. This paper computes the frequency spectrum of relic gravitational radiation from a turbulent source of the stationary Kolmogoroff form which acts for a given duration, making no other approximations. We also show that the limit of long source wavelengths, commonly employed in aeroacoustic problems, is an excellent approximation. The gravitational waves from cosmological turbulence around the electroweak energy scale will be detectable by future space-based laser interferometers for a substantial range of turbulence parameters.

Figures (1)

• Figure 1: The spectrum of gravitational radiation from turbulence. The three solid lines are for different Mach numbers, with ${\rm M}=0.01$, ${\rm M}=0.1$, and ${\rm M}=1$ from lowest to highest amplitude. Note that these three cases have also been scaled by a factor of ${\rm M}^{-3/2}$ for display, since this is how the low-frequency tail scales with ${\rm M}$. The dotted lines, which are virtually indistinguishable from the solid lines except for the ${\rm M}=1$ case, show the $k=0$ approximation to the gravitational wave source.