The Spectrum of Gravitational Radiation from Primordial Turbulence

TL;DR

This paper calculates the detailed frequency spectrum of gravitational waves generated by primordial turbulence in the early universe, showing potential detectability by future space-based interferometers.

Contribution

It provides a comprehensive computation of the gravitational wave spectrum from stationary Kolmogoroff turbulence without simplifying assumptions, extending previous estimates.

Findings

Relic gravitational waves from early universe turbulence are potentially detectable.

The long-wavelength approximation is validated for cosmological turbulence.

The spectrum depends on turbulence parameters and energy injection scale.

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.