Perturbative Degrees of Freedom in Loop Quantum Gravity: Anisotropies

TL;DR

This paper explores how small anisotropic perturbations can be incorporated into loop quantum cosmology, providing insights into their effects on the dynamics and singularity resolution, with implications for cosmological models.

Contribution

It introduces a perturbative approach to include anisotropies in loop quantum cosmology, bridging symmetry reduction and non-symmetric degrees of freedom in a background independent setting.

Findings

Perturbative anisotropies can be included in loop quantum cosmology dynamics.

Small non-symmetric degrees of freedom do not conclusively resolve singularities.

Perturbative approach may lead to misleading conclusions about singularity resolution.

Abstract

The relation between an isotropic and an anisotropic model in loop quantum cosmology is discussed in detail, comparing the strict symmetry reduction with a perturbative implementation of symmetry. While the latter cannot be done in a canonical manner, it allows to consider the dynamics including the role of small non-symmetric degrees of freedom for the symmetric evolution. This serves as a model for the general situation of perturbative degrees of freedom in a background independent quantization such as loop quantum gravity, and for the more complicated addition of perturbative inhomogeneities. While being crucial for cosmological phenomenology, it is shown that perturbative non-symmetric degrees of freedom do not allow definitive conclusions for the singularity issue and in such a situation could even lead to wrong claims.