(Non) singular Kantowski-Sachs Universe from quantum spherically reduced matter

TL;DR

This paper derives quantum-corrected solutions for the Kantowski-Sachs universe using spherical reduction and one-loop effective action, revealing non-singular cosmologies with quantum effects and classical singular solutions.

Contribution

It provides analytical solutions for quantum-corrected Kantowski-Sachs cosmology from 2D dilaton gravity, including non-singular models and purely quantum solutions with no classical counterparts.

Findings

Quantum-corrected KS cosmology can be non-singular.

Purely quantum solutions exist without classical limits.

Classical singular solutions are recovered in certain limits.

Abstract

Using s-wave and large N approximation the one-loop effective action for 2d dilaton coupled scalars and spinors which are obtained by spherical reduction of 4d minimal matter is found. Quantum effective equations for reduced Einstein gravity are written. Their analytical solutions corresponding to 4d Kantowski-Sachs (KS) Universe are presented. For quantum-corrected Einstein gravity we get non-singular KS cosmology which represents 1) quantum-corrected KS cosmology which existed on classical level or 2)purely quantum solution which had no classical limit. The analogy with Nariai BH is briefly mentioned. For purely induced gravity (no Einstein term) we found general analytical solution but all KS cosmologies under discussion are singular. The corresponding equations of motion are reformulated as classical mechanics problem of motion of unit mass particle in some potential V.