A known supersymmetric hybrid inflation model, with soft supersymmetry-breaking and supergravity terms included, can produce a spectral index n_s in 0.96 to 0.98, consistent with ACT DR6, Planck 2018 and BK18, by choosing the model parameter kappa.
Inflation and Supersymmetry Breaking
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We study the connection between inflation and supersymmetry breaking in the context of an O'Raifeartaigh model which can account for both hybrid inflation and a true vacuum where supersymmetry is spontaneously broken. For a weakly coupled inflaton field, the dynamics during the inflationary phase can be determined by the supersymmetry breaking scale $M_S\sim 10^{10}$ GeV, even if $H_I >> m_{3/2}$. The spectrum of density fluctuations is then almost scale invariant, with a spectral index $n-1={\cal O}(M_G^2/M_P^2)$. The mass parameter $M_G$ of the O'Raifeartaigh model is determined by the COBE normalization for the cosmic microwave background to be the grand unification scale, $M_G \sim 10^{16}$ GeV.
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Supersymmetric Hybrid Inflation in light of Atacama Cosmology Telescope Data Release 6, Planck 2018 and LB-BK18
A known supersymmetric hybrid inflation model, with soft supersymmetry-breaking and supergravity terms included, can produce a spectral index n_s in 0.96 to 0.98, consistent with ACT DR6, Planck 2018 and BK18, by choosing the model parameter kappa.