Relic gravitational waves from colliding bubbles and cosmic turbulence

Abstract

A stochastic background of gravitational waves can be generated during a cosmological first order phase transition, at least by two distinct mechanisms: collisions of true vacuum bubbles and turbulence in the cosmic fluid. I compare these two contributions, analyzing their relative importance for a generic phase transition. In particular, a first order electroweak phase transition is expected to generate a gravitational wave signal peaked at a frequency which today falls just within the band of the planned space interferometer LISA. For this transition, I find constraints for the relevant parameters in order to produce a signal within the reach of the sensitivity of LISA. The result is that the transition must be strongly first order, alpha > 0.2. In this regime the signal coming from turbulence dominates over that from colliding bubbles.

Figures (2)

• Figure 1: The total GW spectrum $h _0 ^2 \Omega_{\rm gw}$vs. frequency (in mHz), from a generic first order phase transition, for three different values of $\alpha$, together with the sensitivity curve of LISA (bold line) LISA. $\beta / H_*$ is set to 100 and $T_*$ to 100 GeV: different values would only give a global rescaling of the spectra, without affecting their shape.
• Figure 2: The shaded regions show the values of $\alpha$ and $\beta/H_*$ for which the total GW signal coming from a first order electroweak phase transition is above the LISA sensitivity curve. $T_*$ is fixed to 100 GeV. The top plot refers to ordinary Navier Stokes turbulence, while the bottom one to MHD turbulence. In the region labelled by 1 only GWs from turbulence are visible at LISA. In 2 both peaks (from turbulence and from bubble collision) are visible. In 3 the bubble collisions peak is below the high frequency tail coming from turbulence, but nevertheless there exists a frequency range in which the bubble collision contribution is recognizable by the slope change in the signal. In 4 (in the bottom plot) such slope change takes place at too high frequecies, where the GW signal is below the LISA sensitivity, and therefore, the bubble collision signal is completely overwhelmed by the turbulence one in the frequency window interesting for LISA.