Negative modes of Coleman-De Luccia bounces

TL;DR

This paper analyzes negative modes in Coleman-De Luccia bounces to understand vacuum decay in de Sitter space, revealing different behaviors depending on the bounce size and nucleation rate, and clarifying previous anomalies.

Contribution

It provides a detailed analysis of negative modes in Coleman-De Luccia bounces, identifying regimes based on nucleation rate and confirming previous results about anomalous modes.

Findings

Two regimes for small bounces: flat spacetime behavior at high nucleation rates and deviations at low rates.

Confirmation of anomalous negative modes on the bounce wall for horizon-sized bounces.

Evidence supporting the absence of negative modes in nearly degenerate vacua cases.

Abstract

We investigate the negative modes about Coleman-De Luccia bounces governing vacuum transitions in de Sitter space, with the goal of gaining physical insight into the various anomalous results associated with these that have been reported in the literature. For the case of bounces with radii much less that the horizon distance $H^{-1}$ we find two distinct regimes, distinguished by the magnitude of the bubble nucleation rate $\Gamma$. If $\Gamma/H^4 \gg 1$, then the behavior of the modes contributing to the determinant factors in $\Gamma$ is much as in flat spacetime, and the calculation of $\Gamma$ goes over smoothly to the flat spacetime calculation as the gravitational coupling is taken to zero. This is not the case if $\Gamma/H^4 \ll 1$. These two regimes correspond to the two possible outcomes of de Sitter vacuum decay --- either a rapidly completed transition or non-percolation and eternal inflation. For bounces with radii comparable to the horizon length, we confirm previous results concerning anomalous negative modes with support on the bounce wall. We also find further evidence supporting previous claims, based on thin-wall arguments, of the absence of expected negative modes for a class of bounces that arises when the initial and final vacua are nearly degenerate.