An Exact Tunneling Solution in a Simple Realistic Landscape

TL;DR

This paper provides an exact analytical tunneling solution in a realistic potential landscape, avoiding common approximations, applicable to inflationary cosmology scenarios, and discusses potential inclusion of gravity effects.

Contribution

It introduces a new exact tunneling solution in a piecewise linear and quadratic potential without relying on the thin-wall approximation.

Findings

Solution valid for all barrier regimes

Applicable to realistic inflationary landscapes

Provides a basis for including gravitational effects

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 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 shortly comment on the inclusion of gravity.