Simplified Smooth Hybrid Inflation in Supersymmetric SU(5)

A scheme of simplified smooth hybrid inflation is realized in the framework of supersymmetric $SU(5)$. The smooth model of hybrid inflation provides a natural solution to the monopole problem that appears in the breaking of $SU(5)$ gauge symmetry. The supergravity corrections with nonminimal K\"ahler potential are shown to play important role in realizing inflation with a red-tilted scalar spectral index $n_s <1$, within Planck's latest bounds. As compared to shifted model of hybrid inflation, relatively large values of the tensor-to-scalar ratio $r \lesssim 0.01$ are achieved here, with nonminimal couplings $-0.05 \lesssim \kappa_S \lesssim 0.01$ and $-1 \lesssim \kappa_{SS} \lesssim 1$ and the gauge symmetry-breaking scale $M \simeq (2.0 - 16.7) \times 10^{16}$ GeV.