Truly Lorentzian quantum cosmology. II. Exact formula and effective geometries

Description

Title: Truly Lorentzian quantum cosmology. II. Exact formula and effective geometries

Author: Ding Jia

Abstract: We derive a closed-form expression for the path integral over Lorentzian metrics in the homogeneous and isotropic minisuperspace setting. The result corrects many previous works by a reflection term, which is a weighted product of a path integral from the initial boundary value to zero, times a path integral from zero to the final boundary value. As an implication, we can now continue Einstein’s equation through singularities at the level of effective classical geometries. To achieve this, the Einstein-Hilbert action and a sum over Lorentzian metrics is all one needs.

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Version history

• Original versions: Article v1.0; Notebook v1.0