Unitarity-Safe Models of Non-Minimal Inflation in Supergravity

We show that models of chaotic inflation based on the phi^p potential and a linear non-minimal coupling to gravity, fR=1+cR phi, can be done consistent with data in the context of Supergravity, retaining the perturbative unitarity up to the Planck scale, if we employ logarithmic Kahler potentials with prefactors -p(1+n) or -p(n+1)-1, where -0.035<= n<=0.007 for p=2 or -0.0145<= n<=0.006 for p=4. Focusing, moreover, on a model employing a gauge non-singlet inflaton, we show that a solution to the mu problem of MSSM and baryogenesis via non-thermal leptogensesis can be also accommodated.