Discrete R -symmetry, various energy scales, and gravitational waves

Abstract

We present a supersymmetric model where energy scales of a discrete $R$-symmetry breaking ($Z_{6R}$) and cosmic inflation are commonly attributed to the confinement scale of a hidden $Sp(2)$ strong dynamics. Apart from these, SUSY-breaking scale, the Higgsino mass and the right-handed neutrino masses are all shown to stem from $Z_{6R}$ breaking scale inferred from CMB observables. We will show that the model is characterized by the SUSY-breaking soft mass $m_{\rm soft}\simeq100-1000{\rm TeV}$ and the reheating temperature $T_{\rm rh}\simeq10^{9}{\rm GeV}$. Then we discuss how these predictions of the model can be tested with the help of the spectrum of the gravitational wave induced by the short-lived cosmic string present during the reheating era.