Gravitational Radiation from Primordial Helical Inverse Cascade MHD Turbulence

TL;DR

The paper addresses gravitational wave production from primordial helical MHD turbulence generated by electroweak bubble collisions, using two inverse cascade models to characterize the late stage of turbulence. It applies a aero-acoustic real-space formalism to obtain the GW spectrum, predicting two notable peaks: a direct cascade peak at high frequency and an inverse cascade peak at the Hubble frequency f_H, with the latter often dominating the signal. For plausible phase transition parameters the spectrum shows weak model dependence and strong polarization, making the signal potentially detectable by LISA and offering a direct handle on parity violation via magnetic helicity. The analysis also highlights the applicability of the framework to other phase transitions such as the QCD transition and underscores the astrophysical significance of helicity in shaping primordial gravitational wave backgrounds.

Abstract

We consider the generation of gravitational waves by primordial helical inverse cascade magnetohydrodynamic (MHD) turbulence produced by bubble collisions at the electroweak phase transition. We extend the previous study \cite{kgr08} by considering both currently discussed models of MHD turbulence. For popular electroweak phase transition parameter values, the generated gravitational wave spectrum is only weakly dependent on the MHD turbulence model. Compared to the unmagnetized electroweak phase transition case, the spectrum of MHD-turbulence-generated gravitational waves peaks at lower frequency with larger amplitude and can be detected by the proposed Laser Interferometer Space Antenna

Figures (4)

• Figure 1: The spectrum of the gravitational wave strain amplitude, $h_C(f)$, as a function of the frequency $f$ for a first-order phase transition with $g_* = 100$, $T_* = 100$ GeV, $\alpha = 0.5$, and $\beta = 100 H_\star$, from hydrodynamic Kolmogorov turbulence with zero magnetic helicity (solid lines) and for the two MHD turbulence models, Model A (dash-dotted lines) and Model B (dashed lines). The left panel corresponds to initial magnetic helicity $\zeta_\star =0.15$, while $\zeta_\star=0.05$ in the right panel. In both panels the bold solid line corresponds to the 1-year, $5\sigma$ LISA design sensitivity curve curve including confusion noise from white dwarf binaries whitedwarfs.
• Figure 2: As in Fig. 1, except now $T_\star = 250$ GeV.
• Figure 3: The LISA sensitivity region for Model A in the $\beta/H_*$ and $T_*$ parameter plane for a phase transition with vacuum energy $\alpha=0.1$ (left panel) and $\alpha=0.5$ (right panel) kkgm08. The regions for $\zeta_*=0$ and $\zeta_*=0.15$ coincide at these temperatures for $\alpha=0.1$ (left panel). A point in parameter space is considered detectable if at any frequency its value of $h_c(f)$ is detectable at a signal-to-noise ratio of 5 in a one-year integration, including the confusion noise from white dwarf binaries, based on Refs. curve.
• Figure 4: The LISA sensitivity region for Model A in the $\alpha$ and $T_*$ parameter plane (left panel) with $\beta/H_\star =100$ and $g_\star =100$, and in the $g_\star$ and $T_\star$ parameter plane (right panel) with $\beta/H_\star = 100$ and $\alpha=0.1$. A point in parameter space is considered detectable if at any frequency its value of $h_c(f)$ is detectable at a signal-to-noise ratio of 5 in a one-year integration, including the confusion noise from white dwarf binaries, based on Refs. curve.