Fluctuations about Cosmological Instantons

TL;DR

This paper analyzes quantum fluctuations around bounce solutions in curved spacetime, revealing the behavior of fluctuation determinants and negative modes, which clarify the nature of oscillating instantons beyond standard tunneling interpretations.

Contribution

It extends the fluctuation analysis to curved space and oscillating instantons, providing insights into their negative modes and fluctuation determinants.

Findings

Large l behavior of fluctuation determinants determined.

Oscillating bounces have negative modes in higher partial waves.

Standard bounce has a single negative mode in the s-wave.

Abstract

We study the semiclassical fluctuation problem around bounce solutions for a self-interacting scalar field in curved space. As in flat space, the fluctuation problem separates into partial waves labeled by an integer l, and we determine the large l behavior of the fluctuation determinants, a quantity needed to define a finite fluctuation prefactor. We also show that while the Coleman-De Luccia bounce solution has a single negative mode in the l=0 sector, the oscillating bounce solutions also have negative modes in partial waves higher than the s-wave, further evidence that they are not directly related to quantum tunneling.