Zoology of instanton solutions in flat potential barriers

TL;DR

This paper explores the diverse landscape of instanton solutions in Einstein-scalar theories with flat potential barriers, revealing a complex network of solutions including Hawking-Moss, Coleman-De Luccia, and oscillating instantons, connected through critical solutions.

Contribution

It provides a comprehensive classification and analysis of instanton solutions in flat barrier potentials, highlighting the rich structure and connections among different solution types.

Findings

Identification of various instanton solutions including non-standard types.

Discovery of connections between solutions via critical instantons with zero modes.

The solution space is more intricate and diverse than previously understood.

Abstract

We perform a detailed study of the existence and the properties of O(4)-invariant instanton solutions in Einstein-scalar theory in the presence of flat potential barriers, i.e. barriers where the second derivative of the potential is small at the top of the barrier. We find a whole zoo of solutions: Hawking-Moss, Coleman-De Luccia (CdL), oscillating instantons, asymmetric CdL as well as other non-standard CdL-like solutions with additional negative modes in their spectrum of fluctuations. Our work shows how these different branches of solutions are connected to each other via "critical" instantons possessing an extra zero mode fluctuation. Overall, the space of finite action euclidean solutions to these theories with flat barriers is surprisingly rich and intricate.