Smooth hybrid inflation with low reheat temperature and observable gravity waves in SU(5) × U(1)$_{χ}$ super-GUT

We realize smooth hybrid inflation in the framework of supersymmetric SU(5) × U(1)$_{χ}$ ⊂ SO(10) model which provides a natural solution to the monopole problem appearing in the spontaneous symmetry breaking of SU(5). The breaking of U(1)$_{χ}$ symmetry leaves a residual discrete Z $_{2}$ symmetry, that serves as the MSSM matter parity, realizing the possibility of the lightest supersymmetric particle as a cold dark matter candidate. The d = 5 proton lifetime for the decay p ⟶ K $^{+}$ν̅, mediated by color-triplet Higgsinos is found to satisfy current experimental bounds if split-high scale SUSY scenario is employed. We show that with minimal Kähler potential, the soft supersymmetry breaking terms play a vital rôle in bringing the scalar spectral index ns within the Planck's latest bounds. In a minimal Kähler potential setup, small values of tensor-to-scalar ratio r ≲ 3.5 × 10$^{-7}$ are obtained, whereas the gravitino mass turns out to be in the range that favors PeV scale SUSY but is not sufficiently high to avoid the d = 5 proton decay. A non-minimal Kähler potential including higher order corrections is required to realize successful inflation with central value of scalar spectral index ns = 0.9655, large tensor modes r ≲ 0.056 and a low reheat temperature (3 × 10$^{6}$ ≲ Tr ≲ 6.5 × 10$^{7}$) GeV consistent with leptogenesis and baryogenesis.