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

Abstract

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 $p\to K^{+}\bar{\nu }$, 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 Kähler potential, the soft supersymmetry breaking terms play a vital rôle in bringing the scalar spectral index $n_s$ within the Planck's latest bounds. In a minimal Kähler potential setup, small values of tensor-to-scalar ratio $r\lesssim 3.5\times 10^{-7}$ 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 $n_s=0.9655$, large tensor modes $r\lesssim 0.056$ and a low reheat temperature $(3\times 10^6\lesssim T_r\lesssim 6.5\times 10^7)$ GeV consistent with leptogenesis and baryogenesis.

Comments: 23 pages, 6 figures