The Overshoot Problem in Inflation after Tunneling

Abstract

We show the absence of the usual parametrically large overshoot problem of small-field inflation if initiated by a Coleman-De Luccia (CDL) tunneling transition from an earlier vacuum in the limit of small inflationary scale compared to the tunneling scale. For low-power monomial exit potentials $V(\varphi )\sim {\varphi }^n,n<4$, we derive an expression for the amount of overshoot. This is bounded from above by the width of the steep barrier traversed after emerging from tunneling and before reaching a slow-roll region of the potential. For $n\ge 4$ we show that overshooting is entirely absent. We extend this result through binomials to a general potential written as a series expansion, and to the case of arbitrary finite initial speed of the inflaton. This places the phase space of initial conditions for small-field and large-field inflation on the same footing in a landscape of string theory vacua populated via CDL tunneling.

14 pages, 4 figures

References in corpus (8)

• The Anthropic Landscape of String Theory
• Holographic Systematics of D-brane Inflation
• Chasing Brane Inflation in String-Theory
• String moduli inflation: an overview
• Challenges for String Cosmology
• Brane Inflation is Attractive
• Brane Inflation and the Overshoot Problem
• Fine-tuning criteria for inflation and the search for primordial gravitational waves

Cited by in corpus (14)

• Inflationary paradigm after Planck 2013
• Multi-field open inflation model and multi-field dynamics in tunneling
• Accidental Inflation in the Landscape
• Testing Realistic $SO(10)$ SUSY GUTs with Proton Decay and Gravitational Waves
• More Exact Tunneling Solutions in Scalar Field Theory
• The Scale of Inflation in the Landscape
• Initial conditions for slow-roll inflation in a random Gaussian landscape
• Inhomogeneous Initial Data and Small-Field Inflation
• Validity of the kink approximation to the tunneling action
• Tensor modes on the string theory landscape
• TwInflation
• A Toy Model For Single Field Open Inflation
• Analytic bounces in d dimensions
• Curvature-Assisted Dynamical Compactification in a Pre-Inflationary Higher-Dimensional Universe