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