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Title:
Lattice refining loop quantum cosmology, anisotropic models, and stability
Authors:
Bojowald, Martin; Cartin, Daniel; Khanna, Gaurav
Affiliation:
AA(Institute for Gravitation and the Cosmos, The Pennsylvania State University, 104 Davey Lab, University Park, Pennsylvania 16802, USA), AA(Naval Academy Preparatory School, 197 Elliot Street, Newport, Rhode Island 02841, USA), AA(Physics Department, University of Massachusetts at Dartmouth, North Dartmouth, Massachusetts 02747, USA)
Publication:
Physical Review D, vol. 76, Issue 6, id. 064018 (PhRvD Homepage)
Publication Date:
09/2007
Origin:
APS
PACS Keywords:
Loop quantum gravity, quantum geometry, spin foams, Lower dimensional models; minisuperspace models, Quantum cosmology
DOI:
10.1103/PhysRevD.76.064018
Bibliographic Code:
2007PhRvD..76f4018B

Abstract

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. The main new effect is an underlying lattice which is being refined during dynamical changes of the volume. In general, this leads to a new feature of dynamical difference equations which may not have constant step-size, posing new mathematical problems. It is discussed how such models can be evaluated and what lattice refinements imply for semiclassical behavior. Two detailed examples illustrate that stability conditions can put strong constraints on suitable refinement models, even in the absence of a fundamental Hamiltonian which defines changes of the underlying lattice. Thus, a large class of consistency tests of loop quantum gravity becomes available. In this context, it will also be seen that quantum corrections due to inverse powers of metric components in a constraint are much larger than they appeared recently in more special treatments of isotropic, free scalar models where they were artificially suppressed.
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