On the classicality and uniqueness in loop quantization of Bianchi-I spacetimes

Abstract

In loop quantum cosmology, ambiguities in the Hamiltonian constraint can result in models with varying phenomenological predictions. In the homogeneous isotropic models, these ambiguities were settled, and the improved dynamics was found to be a unique and phenomenologically viable choice. This issue has remained unsettled on the inclusion of anisotropies, and in the Bianchi-I model there exist two generalizations of isotropic improved dynamics. In the first of these, labelled as $\bar \mu$ quantization, the edge length of holonomies depends on the inverse of the directional scale factor. This quantization has been favored since it results in universal bounds on energy density and anisotropic shear, and can be viably formulated for non-compact as well as compact spatial manifolds. However, there exists an earlier quantization, labelled as $\bar \mu'$ quantization, where edge lengths of holonomies depend on the inverse of the square root of directional triads. This quantization is also non-singular and so far believed to yield a consistent physical picture for spatially compact manifolds. We examine the issue of the physical viability of these quantizations for different types of matter in detail by performing a large number of numerical simulations. Our analysis reveals certain limitations which have so far remained unnoticed. We find that while being non-singular, the $\bar \mu'$ quantization suffers from a surprising problem where one of the triad components and associated polymerized term retains Planckian character even at large volumes. As a result, not only is the anisotropic shear not preserved across the bounce, which is most highlighted in the vacuum case, but the universe can exhibit an unexpected cyclic evolution. These problematic features are absent from the $\bar \mu$ quantization leaving it as the only viable prescription for loop quantizing the Bianchi-I model.