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Loop Quantum Cosmology of Diagonal Bianchi Type I model: simplifications and scaling problems
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abstract
A simplified theory of the diagonal Bianchi type I model coupled with a massless scalar field in loop quantum cosmology is constructed according to the $\bar{\mu}$ scheme. Kinematical and physical sectors of the theory are under good analytical control as well as the scalar constraint operator. Although it is possible to compute numerically the nonsingular evolution of the three gravitational degrees of freedom, the naive implementation of the $\bar{\mu}$ scheme to the diagonal Bianchi type I model is problematic. The lack of the full invariance of the theory with respect to the fiducial cell and fiducial metric scaling causes serious problems in the semiclassical limit of the theory. Because of this behavior it is very difficult to extract reasonable physics from the model. The weaknesses of the implementation of the $\bar{\mu}$ scheme to the Bianchi I model do not imply limitations of the $\bar{\mu}$ scheme in the isotropic case.
Forward citations
Cited by 2 Pith papers
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On the dynamics of single-vertex states in quantum-reduced loop gravity
The Hamiltonian of single-vertex states in quantum-reduced loop gravity formally matches Bianchi I loop quantum cosmology, and an analogy suggests adding a non-trivial Lorentzian curvature term to the cosmology Hamiltonian.
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Quantum-reduced loop gravity: New perspectives on the kinematics and dynamics
The paper reformulates quantum-reduced loop gravity with a master constraint operator and finds that its single-node Hamiltonian matches the Bianchi I loop quantum cosmology Hamiltonian.
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