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We consider an initial condition problem in a nearly quadratic chaoticinflation model in supergravity. We introduce shift symmetry breaking not onlyin the superpotential but also in the Kahler potential. In this model theinflaton potential is nearly quadratic for inflaton field values around thePlanck scale, but deviates from the quadratic one for larger field values. As aresult, the prediction on the tensor-to-scalar ratio can be smaller than thatof a purely quadratic model. Due to the shift symmetry breaking in the Kahlerpotential, the inflaton potential becomes steep for large inflaton fieldvalues, which may prevent inflation from naturally taking place in a closeduniverse. We estimate an upper bound on the magnitude of the shift symmetrybreaking so that inflation takes place before a closed universe with a Plancklength size collapses, which yields a lower bound on the tensor-to-scalarratio, $r \mathop{}_{\textstyle \sim}^{\textstyle >} 0.1$.

physics letters b

Lower bound of the tensor-to-scalar ratio $r \mathop{}_{\textstyle  \sim}^{\textstyle >} 0.1$ in a nearly quadratic chaotic inflation model in  supergravity