An exact tunneling solution in a simple realistic landscape

Abstract

We present an analytical solution for the tunneling process in a piecewise linear and quadratic potential which does not make use of the thin-wall approximation. A quadratic potential allows for the smooth attachment of various slopes exiting into the final minimum of a realistic potential. Our tunneling solution thus serves as a realistic approximation to situations such as populating a landscape of slow-roll inflationary regions by tunneling, and it is valid for all regimes of the barrier parameters. We comment briefly on the inclusion of gravity.