Spectrum of gravitational radiation from primordial turbulence

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.

Figure 1

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