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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 Kähler potential are crucial to realize the central value of the scalar spectral index ns≃0.96 consistent with the 7 yr WMAP data. The tensor to scalar ratio r is quite small, taking on values r≲10-5. 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. [ABSTRACT FROM AUTHOR]

We show how successful supersymmetric hybrid inflation is realized in realistic models where the resolution of the minimal supersymmetric standard model µ problem is intimately linked with axion physics. The scalar fields that accompany the axion, such as the saxion, are closely monitored during and after inflation to ensure that the axion isocurvature perturbations lie below the observational limits. The scalar spectral index n s ≃ 0.96 - 0.97, while the tensor-to-scalar ratio r, a canonical measure of gravity waves, lies well below the observable range in our example. The axion domain walls are inflated away, and depending on the axion decay constant f a and the magnitude of the µ parameter, the axions and/or the lightest supersymmetric particle compose the dark matter in the Universe. Nonthermal leptogenesis is naturally implemented in this class of models. [ABSTRACT FROM AUTHOR]