Inhomogeneous instability in quantum cosmology?
Description
Title: Inhomogeneous instability in quantum cosmology?
Author: Ding Jia
Abstract: In a series of interesting works, Feldbrugge, Lehners, and Turok (FLT) applied Picard-Lefschetz theory to real time path integrals for quantum cosmology, and identified certain inhomogeneous and anisotropic instabilities for models that set the initial size of the universe to zero. In a previous paper, we showed that the anisotropic instability is actually absent by a careful analysis of the relevant saddle paths. In this work, we show that the inhomogeneous instability is also actually absent. Integrating out the squared scale factor and the scalar field variables generates a branch cut in the complex lapse plane that overlap with the original integration contour. While FLT let the contour pass above the branch cut, we show that the correct contour should go below the cut according to both Picard-Lefschetz theory and the iε prescription. For this contour there is no inhomogeneous instability. Consequently, several follow-up works in the literature for sophisticated proposals in quantum cosmology are ill-motivated. As things currently stand, metric variable path integrals with real contours and unsophisticated boundary conditions still constitute a promising avenue for progress in quantum cosmology.
Version history
- Original versions: Article v1.0; Notebook v1.0
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