Frictionless UV-finite Instantons in Curved Spacetime

TL;DR

This paper introduces a new class of UV-complete, frictionless instanton solutions in curved spacetime that describe false vacuum decay, with finite quantum fluctuation contributions after renormalization, potentially impacting quantum field theory in curved backgrounds.

Contribution

It presents a novel class of UV-complete instantons in curved spacetime with frictionless dynamics and finite quantum corrections, expanding understanding of vacuum decay processes.

Findings

Identified UV-complete instantons with frictionless dynamics in curved spacetime.

Computed finite quantum fluctuation prefactors using WKB and Gelfand-Yaglom methods.

Discussed implications of frictionless UV-finite instantons for vacuum decay.

Abstract

We identify a new class of UV-complete instanton solutions that describe the false vacuum\- decay of a real scalar field in a particular curved spacetime background. To this end, we consider a simple scalar theory with a Coleman potential and calculate the Euclidean action $S_{\text{E}}$ by assuming an O(4)-symmetric curved spacetime. The function $a(r)$ dictating the geometry of spacetime may consistently be chosen to be a constant, thereby eliminating the drag forces from the equations of motion and ensuring that the gravitational backgrounds of both the false vacuum and bounce solutions are identical. By employing standard WKB and Gelfand-Yaglom methods, we compute the corresponding prefactor due to quantum fluctuations around this frictionless bounce solution which becomes UV finite after renormalization. The possible consequences of such frictionless UV-finite instantons are discussed.