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

We present a supersymmetric model where energy scales of a discrete <math display="inline"><mi>R</mi></math>-symmetry breaking (<math display="inline"><msub><mi>Z</mi><mrow><mn>6</mn><mi>R</mi></mrow></msub></math>) and cosmic inflation are commonly attributed to the confinement scale of a hidden <math display="inline"><mi>S</mi><mi>p</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></math> strong dynamics. Apart from these, the supersymmetry-breaking scale, the Higgsino mass, and the right-handed neutrino masses are all shown to stem from the <math display="inline"><msub><mi>Z</mi><mrow><mn>6</mn><mi>R</mi></mrow></msub></math> breaking scale inferred from cosmic microwave background observables. We will show that the model is characterized by the supersymmetry-breaking soft mass <math display="inline"><msub><mi>m</mi><mrow><mi>soft</mi></mrow></msub><mo>≃</mo><mn>100</mn><mi>–</mi><mn>1000</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> and the reheating temperature <math display="inline"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>rh</mi></mrow></msub><mo>≃</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>9</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>. 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.