Perturbative Degrees of Freedom in Loop Quantum Gravity: Anisotropies

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.

32 pages

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Cited by in corpus (14)

• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Loop Quantum Cosmology
• Loop quantum cosmology of Bianchi I models
• Loop quantum cosmology of Bianchi type IX models
• Loop quantum cosmology and inhomogeneities
• Lattice refining loop quantum cosmology, anisotropic models and stability
• Stepping out of Homogeneity in Loop Quantum Cosmology
• Cosmic recall and the scattering picture of Loop Quantum Cosmology
• Effective Dynamics, Big Bounces and Scaling Symmetry in Bianchi Type I Loop Quantum Cosmology
• Quantum nature of cosmological bounces
• Gauge invariant perturbations around symmetry reduced sectors of general relativity: applications to cosmology
• Gravity, Geometry and the Quantum
• 2+1 dimensional loop quantum cosmology of Bianchi I models
• On some $\overrightarrow{p(x)}$ anisotropic elliptic equations in unbounded domain