Fluctuations about Cosmological Instantons

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.