Smooth Hybrid Inflation with Low Reheat Temperature and Observable Gravity Waves in $SU(5) \times U(1)_{\chi}$ Super-GUT

Understand

We realize smooth hybrid inflation in the framework of supersymmetric $SU(5) \times U(1)_{\chi}\subset SO(10)$ model which provides a natural solution to the monopole problem appearing in the spontaneous symmetry breaking of $SU(5)$.

• The breaking of $U(1)_{\chi}$ 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 $p \rightarrow K^+ \bar{\nu}$, 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 K\"ahler potential, the soft supersymmetry breaking terms play a vital r\^ole in bringing the scalar spectral index $n_s$ within the Planck's latest bounds.