Truly Lorentzian quantum cosmology. III. Scalar field coupling

Title: Truly Lorentzian quantum cosmology. III. Scalar field coupling

Author: Ding Jia

Abstract: In prequel works we compared real time path integrals for minisuperspace quantum cosmology with and without a Lorentzian constraint. It was found that restricting the sum to metrics of the Lorentzian signature gives rise to new stationary paths for the action. These paths indicate how the effective geometries of the quantum model continue through the cosmological singularity by bouncing once off the singularity. In the present work, we improve the pure gravity model by matter coupling. For a scalar field with hyperbolic potentials, the Lorentzian constraint again gives rise to new stationary paths significant contributions to the path integral. The bounce in both matter and gravitational degrees of freedom forms an analogy with particle corner collision where multiple constraints are triggered simultaneous. A sequential limit regularization implies velocity-symmetric bounces at the cosmological singularity.

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Version history

• Original versions: Article v1.0; Notebook v1.0
• Article v1.1 and Notebook v1.1: minor updates to improve presentation and correct typos
• Article v2.0 and Notebook v2.0: major updates use variational inequality formalism and sequential limit for corner bounce to derive symmetric bounce solutions, and rule out asymmetric bounce solutions in the previous version.