Polarized Cosmological Gravitational Waves from Primordial Helical Turbulence

TL;DR

It is shown that helical turbulence produced during a first-order phase transition generates circularly polarized cosmological gravitational waves (GWs), and the characteristic frequency of these GWs for an extreme case of the phase transition model is around 10(-3)-10(-2) Hz.

Abstract

We show that helical turbulence produced during a first-order phase transition generates circularly polarized cosmological gravitational waves (GWs). The characteristic frequency of these GWs for an extreme case of the phase transition model is around $10^{-3}$ --- $10^{-2}$ Hz with an energy density parameter as high as $10^{-12}$ --- $10^{-11}$. The possibility of detection is briefly discussed.

Figures (1)

• Figure 1: GW polarization degree ${\mathcal{P}}(K, t_{\rm{fi}})$, Eq. (\ref{['degree']}), as a function of scaled wave number $K=k/k_S$ relative to the large-scale wave number $k_S$ on which energy is pumped into the turbulence. This is evaluated at time $t_{\rm{fi}}$, after the turbulence has switched off, and remains unchanged to the present epoch. It has been computed for a damping wave number $k_D=10k_S$. Three pairs of curves are shown. Solid lines correspond to the amplitude ratio $A_0/S_0=1$ (maximally helical turbulence helicity2), dashed lines to $A_0/S_0=0.5$, and dot-dashed lines are for $A_0/S_0 =0.2$. The upper line in each pair corresponds to HT turbulence with $n_S=n_H=-13/3$MC96DG01 and the lower line to HK turbulence with $n_S=-11/3$ and $n_H=-14/3$L. Even for helical turbulence with $A_0/S_0 \leq 0.5$, for large wave numbers $k \sim k_D$, $n_S=n_H=-13/3$ is unlikely so the large $K$ part of the lower dashed and dot-dashed HT curves are unrealistic. The large $k \sim k_D$ decay of the HK curves is a consequence of vanishing helicity transfer at large $k$k73.