Gravitational waves as a probe of the SUSY scale

We investigate the sources of the Hubble-induced mass for a flat direction in supersymmetric theories and show that the sign of the Hubble-induced mass generally changes just after the end of inflation. This implies that global cosmic strings generally form after the end of inflation in a wide class of supersymmetric models, including the minimal supersymmetric Standard Model. The cosmic strings emit gravitational waves whose frequency corresponds to the Hubble scale, until they disappear when the Hubble parameter decreases down to the soft mass of the flat direction. As a result, the peak frequency of gravitational waves is related to the supersymmetric scale. The observation of this gravitational wave signal, in conjunction with results from collider experiments and dark matter searches, can yield information of supersymmetry-breaking parameters.

Figure 1

Evolution of GW spectra obtained by numerical calculations. We show the obtained spectra at $\tau H_i=14$ (red line), $\tau H_i=36$ (green line), and $\tau H_i=100$ (magenta line). We take $n=4$, $c_H=15$, and $m_{\varphi }/H_i=5\times {10}^{-4}$. The blue (dashed) curve represents the contour of the peak frequency and the peak GW energy density for the case of $m_{\varphi }/H_i=5\times {10}^{-4}$ (0). The red dashed curve represents an analytic estimation given by Eqs. (10) and (11) with $k$-independent $T_{ij}^{\mathrm{TT}}$.

Figure 2

GW spectra generated by cosmic strings and sensitivities of planned interferometric detectors. We plot the cases with $m_{\varphi }={10}^2\mathrm{GeV}$ (red dashed curve) and $m_{\varphi }={10}^3\mathrm{GeV}$ (red dot-dashed curve) for $T_{\mathrm{RH}}={10}^9\mathrm{GeV}$. We also plot the case with $m_{\varphi }={10}^2$ and $T_{\mathrm{RH}}={10}^7\mathrm{GeV}$ (blue dashed curve). We have assumed $M_{*}^2/M_{\text{Pl}}^2=0.1$, $n=4$, and $c_H^{\prime }=a_H^{\prime }=1$.