2007
DOI: 10.1103/physrevd.76.064018
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Lattice refining loop quantum cosmology, anisotropic models, and stability

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… Show more

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Cited by 96 publications
(184 citation statements)
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“…Also the rate of change of correction terms during cosmic evolution depends on the precise state and in particular its refinement. From the tensor mode analysis we have provided further evidence that discrete graph states of loop quantum gravity must be refined during evolution, supporting the results of [28,25,44,45,46]. Details will also determine the precise rate of varying speeds of light and gravitational waves.…”
Section: Discussionmentioning
confidence: 63%
“…Also the rate of change of correction terms during cosmic evolution depends on the precise state and in particular its refinement. From the tensor mode analysis we have provided further evidence that discrete graph states of loop quantum gravity must be refined during evolution, supporting the results of [28,25,44,45,46]. Details will also determine the precise rate of varying speeds of light and gravitational waves.…”
Section: Discussionmentioning
confidence: 63%
“…The effective dynamics inμ -scheme, by contrast, is completely independent of V as is the classical dynamics. (The issue of dependence on V may be related to the instability ofμ-scheme indicated in [15].) In case that the physical size of V has a global meaning (such as in the compactified Bianchi I model or the finite sized homogeneous patches in BKL scenario), the condition for the bounce occurrence can be rephrased: In µ/μ -scheme (respectively), the physical area/volume of the surfaces/bulk of V gets bounced when it undergoes the Planck regime (times a numerical value) measured by the reference of the momentum p φ .…”
Section: Discussionmentioning
confidence: 99%
“…In particular, µ-scheme is suggested in [7], since in the construction for the full theory of LQC the Hamiltonian constraint in µ-scheme gives a difference equation in terms of affine variables and therefore the well-developed framework of the spatially flat-isotropic LQC can be straightforwardly adopted. (However, it is argued in [15] thatμ-scheme may lead to an unstable difference equation.) By contrast,μ -scheme does not admit the required affine variables and the full LQC of it is very difficult to construct.…”
Section: )mentioning
confidence: 99%
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“…It is clear that as constants they would not influence the recurrence behavior of the difference equation, although specific solutions certainly depend on their values. However, in general δ 1 and δ 2 may not be constant but be functions of µ 1 and µ 2 ; this captures the way in which the discrete structure of a state underlying spatial expansion and contraction in loop quantum gravity is being refined dynamically [26,36,37]: at larger µ I , an increment of the total size by a Planck-scale amount has a weaker relative influence on the geometry. As a consequence, δ I decrease with increasing spatial extensions.…”
Section: B Quantum Dynamics: the Hamiltonian Constraintmentioning
confidence: 99%