Triangulated loop quantum cosmology: Bianchi IX universe and inhomogeneous perturbations

Journal Article · Mon Mar 15 04:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.064019· OSTI ID:21409407

Battisti, Marco Valerio; Marciano, Antonino; Rovelli, Carlo ^[1]

---

1. Centre de Physique Theorique, Case 907 Luminy, 13288 Marseille (France)

We develop the triangulated version of loop quantum cosmology, recently introduced in the literature. We focus on the dipole cosmology, where space is a three-sphere and the triangulation is formed by two tetrahedra. We show that the discrete fiducial connection has a simple and appealing geometrical interpretation and we correct the ansatz on the relation between the model variables and the Friedmann-Robertson-Walker scale factor. The modified ansatz leads to the convergence of the Hamiltonian constraint to the continuum one. We then ask which degrees of freedom are captured by this model. We show that the model is rich enough to describe the (anisotropic) Bianchi IX universe, and give the explicit relation between the Bianchi IX variables and the variables of the model. We discuss the possibility of using this path in order to define the quantization of the Bianchi IX universe. The model contains more degrees of freedom than Bianchi IX, and therefore captures some inhomogeneous degrees of freedom as well. Inhomogeneous degrees of freedom can be expanded in representations of the SU(2) Bianchi IX isometry group, and the dipole model captures the lowest integer representation of these, connected to hyperspherical harmonic of angular momentum j=1.

• OSTI ID: 21409407
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 6 Vol. 81; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
79 ASTRONOMY AND ASTROPHYSICS
ANGULAR MOMENTUM
ANISOTROPY
CAPTURE
CONVERGENCE
COSMOLOGY
DEGREES OF FREEDOM
DIPOLES
DISTURBANCES
HAMILTONIANS
LIE GROUPS
MATHEMATICAL OPERATORS
MULTIPOLES
PERTURBATION THEORY
QUANTIZATION
QUANTUM OPERATORS
SIMULATION
SPACE
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS
UNIVERSE