Semiclassical singularity is compatible with quantum singularity avoidance
Description
Title: Semiclassical singularity is compatible with quantum singularity avoidance
Author: Ding Jia
Abstract: In quantum gravity, singularity avoidance at the quantum level is commonly expected to imply singularity avoidance at the effective semiclassical level. Although numerous models support this case, there has been no general proof. In this paper, we show that the expectation is actually not true in general. To this end, we draw a strict distinction among Lorentzian, quasi-Lorentzian, and unconstrained models, which differ by the integration domains in the scale factors or squared scale factors. When a certain symmetry condition applies, the saddle points can be found by the method of image previously employed to study path integrals on constrained domains. When the symmetry condition does not apply, the saddle points can be found by variation within the constraint boundary. In various isotropic and anisotropic minisuperspace quantum cosmology models, it is found that the Lorentzian path integrals can avoid singularities in its sum, but still possess singular bounce saddle points. Mathematically, this is because constraining the integration domain can induce saddle points on the boundary of the domain. Physically, it follows that singular bounce models can arise as effective spacetimes, even for singularity-avoiding fundamental theories.
Version history
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Original versions: Article v1.0; Notebook v1.0
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Article v1.1: color and style of article template updated; no content change
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Article v1.2: correct typos; introduce table of contents; update bibliography; clarify the bouncing saddles for anisotropic case based on new reference
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