Absence of pre-classical solutions in Bianchi I loop quantum cosmology
arXiv:gr-qc/0501016 · doi:10.1103/PhysRevLett.94.111302
Abstract
Loop quantum cosmology, the symmetry reduction of quantum geometry for the study of various cosmological situations, leads to a difference equation for its quantum evolution equation. To ensure that solutions of this equation act in the expected classical manner far from singularities, additional restrictions are imposed on the solution. In this paper, we consider the Bianchi I model, both the vacuum case and the addition of a cosmological constant, and show using generating function techniques that only the zero solution satisfies these constraints. This implies either that there are technical difficulties with the current method of quantizing the evolution equation, or else loop quantum gravity imposes strong restrictions on the physically allowed solutions.
4 pages, no figures, version to appear in PRL
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- Observational issues in loop quantum cosmology
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- Nonsingular Black Holes and Degrees of Freedom in Quantum Gravity
- Classical and Quantum Features of the Mixmaster Singularity
- Numerical loop quantum cosmology: an overview
- Wave functions for the Schwarschild black hole interior
- Perturbative Degrees of Freedom in Loop Quantum Gravity: Anisotropies
- Elements of Loop Quantum Cosmology
- Pre-classical solutions of the vacuum Bianchi I loop quantum cosmology
- Numerical solutions to lattice-refined models in loop quantum cosmology
- Exhaustive investigation of the duration of inflation in effective anisotropic loop quantum cosmology
- Numerical Techniques in Loop Quantum Cosmology
- Instabilities in numerical loop quantum cosmology
- Von Neumann stability of modified loop quantum cosmologies
- Modified Friedmann equation and survey of solutions in effective Bianchi-I loop quantum cosmology
- Quantum Geometry and its Implications for Black Holes
- Separable sequences in Bianchi I loop quantum cosmology
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- Approximate pre-classical solutions in loop quantum cosmology
- Universe scenarios from loop quantum cosmology
- On the Green's function and iterative solutions of Loop Quantum Cosmology
- An Approach to Loop Quantum Cosmology Through Integrable Discrete Heisenberg Spin Chains