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

TL;DR

This paper investigates a supergravity-based inflation model with shift symmetry breaking, showing that the tensor-to-scalar ratio $r$ has a lower bound of approximately 0.1 due to initial condition constraints.

Contribution

It introduces a nearly quadratic chaotic inflation model in supergravity with shift symmetry breaking in both superpotential and Kahler potential, deriving a lower bound on $r$.

Findings

Lower bound on tensor-to-scalar ratio $r \,\sim\> 0.1$.

Shift symmetry breaking affects inflation dynamics and initial conditions.

Constraints prevent inflation in a closed universe smaller than Planck scale.

Abstract

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, $r \mathop{}_{\textstyle \sim}^{\textstyle >} 0.1$.