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.
Anisotropic loop quantum cosmology with self-dual variables
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
A loop quantization of the diagonal class A Bianchi models starting from the complex-valued self-dual connection variables is presented in this paper. The basic operators in the quantum theory correspond to areas and generalized holonomies of the Ashtekar connection and the reality conditions are implemented via the choice of the inner product on the kinematical Hilbert space. The action of the Hamiltonian constraint operator is given explicitly for the case when the matter content is a massless scalar field (in which case the scalar field can be used as a relational clock), and it is shown that the big-bang and big-crunch singularities are resolved in the sense that singular and non-singular states decouple under the action of the Hamiltonian constraint operator.
citation-role summary
background 1
citation-polarity summary
fields
gr-qc 1years
2024 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
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.