Truly Lorentzian quantum cosmology. IV. Kantowski-Sachs

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Title: Truly Lorentzian quantum cosmology. IV. Kantowski-Sachs

Author: Ding Jia

Abstract: In the game of billiards, two balls can be connected either by a direct path, or by paths reflecting off the table edges. From a physics perspective, this is because both types of paths are stationary points of the action. In cosmology, the minisuperspace, like the billiard table, is a bounded domain. In particular, the scale factors are bounded by zero at one end and infinity at the other. The boundaries similarly induce bouncing solutions to the variational equation. These solutions are relevant to path integrals that conform with the minisuperspace boundary. In this work, I identify bouncing saddle points for Kantowski-Sachs path integrals in the pure gravity case. The minisuperspace boundary is partitioned into five parts according to the values of the two scale factors. Only one part supports real bouncing solutions. The bounce takes place at a fixed point, and the solution constitutes a relevant saddle point to Lorentzian and quasi-Lorentzian path integrals. The bouncing saddles are even more significant than the non-bouncing ones, since for certain parameters, the non-bouncing ones become irrelevant while the bouncing ones stay relevant. The results illustrate how bouncing cosmological solutions can arise naturally in anisotropic minisuperspace models, without modifying the Einstein-Hilbert action, or introducing new forms of matter.

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