Absence of preclassical solutions in Bianchi I loop quantum cosmology.
Daniel Cartin,Gaurav Khanna +1 more
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This Letter considers the Bianchi I model, both the vacuum case and the addition of a cosmological constant, and shows using generating function techniques that only the zero solution satisfies constraints on the evolution equation.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 Letter, 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.read more
Citations
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Loop Quantum Cosmology
TL;DR: In this paper, an application of loop quantum cosmology to homogeneous systems, which removes classical singularities, is presented, where the main effects are introduced into effective classical equations, which allow one to avoid the interpretational problems of quantum theory.
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Quantum geometry and the Schwarzschild singularity
TL;DR: In this article, the same quantum geometry effects lead to a resolution of the classical singularity without having to invoke special boundary conditions at the singularity or introduce ad hoc elements such as unphysical matter.
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Spherically symmetric quantum geometry: Hamiltonian constraint
TL;DR: In this paper, the spherically symmetric volume operator is adapted to the quantum dynamics of the model, which further simplifies the volume operator and allows an explicit computation of all matrix elements of the Euclidean and Lorentzian Hamiltonian constraints.
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Lattice refining loop quantum cosmology, anisotropic models, and stability
TL;DR: In this paper, a general class of loop quantizations for anisotropic models is introduced and discussed, which enhances loop quantum cosmology by relevant features seen in inhomogeneous situations.
Journal ArticleDOI
Loop quantum cosmology in Bianchi type I models : Analytical investigation
Dah-Wei Chiou,Dah-Wei Chiou +1 more
TL;DR: In this paper, a comprehensive formulation for loop quantum cosmology in the spatially flat, isotropic model was recently constructed and extended to the anisotropic Bianchi I cosmology, where the scalar field again serves as an internal clock and is treated as emergent time.
References
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TL;DR: In this article, the precise mathematical structure underlying loop quantum cosmology and the sense in which it implements the full quantization program in a symmetry reduced model has been made explicit, thereby providing a firmer mathematical and conceptual foundation to the subject.
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