Kantowski-Sachs spacetime in loop quantum cosmology: bounds on expansion and shear scalars and the viability of quantization

TL;DR

This paper demonstrates that among various loop quantum cosmology quantizations of Kantowski-Sachs spacetime, only the 'improved dynamics' prescription ensures universal bounds on expansion and shear scalars, indicating a consistent quantum geometric behavior.

Contribution

It identifies the 'improved dynamics' as the unique quantization prescription that guarantees bounded scalars and fiducial cell independence in Kantowski-Sachs spacetime.

Findings

Only 'improved dynamics' leads to bounded expansion and shear scalars.

Other prescriptions may produce unbounded scalars and arbitrary quantum effects.

Energy density remains bounded, ruling out pancake singularities.

Abstract

Using effective dynamics, we investigate the behavior of expansion and shear scalars in different proposed quantizations of the Kantowski-Sachs spacetime with matter in loop quantum cosmology. We find that out of the various proposed choices, there is only one known prescription which leads to the generic bounded behavior of these scalars. The bounds turn out to be universal and are determined by the underlying quantum geometry. This quantization is analogous to the so called 'improved dynamics' in the isotropic loop quantum cosmology, which is also the only one to respect the freedom of the rescaling of the fiducial cell at the level of effective spacetime description. Other proposed quantization prescriptions yield expansion and shear scalars which may not be bounded for certain initial conditions within the validity of effective spacetime description. These prescriptions also have a limitation that the "quantum geometric effects" can occur at an arbitrary scale. We show that the `improved dynamics' of Kantowski-Sachs spacetime turns out to be a unique choice in a general class of possible quantization prescriptions, in the sense of leading to generic bounds on expansion and shear scalars and the associated physics being free from fiducial cell dependence. The behavior of the energy density in the `improved dynamics' reveals some interesting features. Even without considering any details of the dynamical evolution, it is possible to rule out pancake singularities in this spacetime. The energy density is found to be dynamically bounded. These results show that the Planck scale physics of the loop quantized Kantowski-Sachs spacetime has key features common with the loop quantization of isotropic and Bianchi-I spacetimes.