Abstract
We analyze the adjoint field inflation in supersymmetric (SUSY) $SU(5)$ model. In minimal SUSY $SU(5)$ hybrid inflation monopoles are produced at the end of inflation. We therefore explore the nonminimal model of inflation based on SUSY $SU(5)$, like shifted hybrid inflation, which provides a natural solution for the monopole problem. We find that the supergravity corrections with nonminimal K\"ahler potential are crucial to realize the central value of the scalar spectral index ${n}_{s}\ensuremath{\simeq}0.96$ consistent with the 7 yr WMAP data. The tensor to scalar ratio $r$ is quite small, taking on values $r\ensuremath{\lesssim}{10}^{\ensuremath{-}5}$. Because of $R$ symmetry massless $SU(3)$ octet and $SU(2)$ triplet supermultiplets are present and could spoil gauge coupling unification. To keep gauge coupling unification intact, light vectorlike particles are added which are expected to be observed at LHC.
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