Gravitational radiation generated by cosmological phase transition magnetic fields

We study gravitational waves generated by the cosmological magnetic fields induced via bubble collisions during the electroweak (EW) and QCD phase transitions. The magnetic field generation mechanisms considered here are based on the use of the fundamental EW minimal supersymmetric and QCD Lagrangians. The gravitational waves spectrum is computed using a magnetohydrodynamic turbulence model. We find that the gravitational wave spectrum amplitude generated by the EW phase transition peaks at a frequency of approximately 1–2 mHz, and is of the order of ${10}^{-20}–{10}^{-21}$; thus this signal is possibly detectable by the Laser Interferometer Space Antenna (LISA). The gravitational waves generated during the QCD phase transition, however, are outside the LISA sensitivity bands.

Figure 1

$h_C(f)$ for the EW phase transitions with $g_{*}=100$, $v_b=1/2$, and $v_0=v_A$ with zero magnetic helicity. Top panel: $T_{*}=80\mathrm{GeV}$ (solid line), $T_{*}=100\mathrm{GeV}$ (dashed line), and $T_{\star }=150\mathrm{GeV}$ (dash-dotted line) with $\beta =100H_{\star }$. Bottom panal: $T_{\star }=100\mathrm{GeV}$ and $\beta =50H_{\star }$ (solid line), $\beta =100H_{\star }$ (dashed line), and $\beta =150H_{\star }$ (dash-dotted line). In both panels the bold solid line corresponds to the 1-year, $5\sigma$ LISA design sensitivity curve [55] including confusion noise from white dwarf binaries, bold dash line [56]. For other parameters, for example, in the case of the low value of $v_b$ [47, 48], the gravitational wave spectrum peak and the amplitude must be rescaled according to Eqs. (24, 25).