118432031
Dynamical eigenfunctions and critical density in loop quantum cosmology
We offer a new, physically transparent argument for the existence of the critical, universal maximum matter density in loop quantum cosmology for the case of a flat Friedmann?Lema?tre?Robertson?Walker cosmology with scalar matter. The argument is based on the existence of a sharp exponential ultraviolet cutoff in momentum space on the eigenfunctions of the quantum cosmological dynamical evolution operator (the gravitational part of the Hamiltonian constraint), attributable to the fundamental discreteness of spatial volume in loop quantum cosmology. The existence of the cutoff is proved directly from recently found exact solutions for the eigenfunctions for this model. As a consequence, the operators corresponding to the momentum of the scalar field and the spatial volume approximately commute. The ultraviolet cutoff then implies that the scalar momentum, though not a bounded operator, is in effect bounded on subspaces of constant volume, leading to the upper bound on the expectation value of the matter density. The maximum matter density is universal (i.e. independent of the quantum state) because of the?linear scaling of the cutoff with volume. These heuristic arguments are supplemented by a new proof in the volume representation of the existence of the maximum matter density. The techniques employed to demonstrate the existence of the cutoff also allow us to extract the large-volume limit of the exact eigenfunctions, confirming earlier numerical and analytical work showing that the eigenfunctions approach superpositions of the eigenfunctions of the Wheeler?DeWitt quantization of the same model. We argue that generic (not just semiclassical) quantum states approach symmetric superpositions of expanding and contracting universes.
119269617
Consistent Probabilities in Wheeler-DeWitt Quantum Cosmology
We give an explicit, rigorous framework for calculating quantum probabilities in a model theory of quantum gravity. Specifically, we construct the decoherence functional for the Wheeler-DeWitt quantization of a flat Friedmann-Robertson-Walker cosmology with a free, massless, minimally coupled scalar field, thus providing a complete decoherent histories formulation for this quantum cosmological model. The decoherence functional is applied to study predictions concerning the model's Dirac (relational) observables; the behavior of semiclassical states and superpositions of such states; and to study the singular behavior of quantum Wheeler-DeWitt universes. Within this framework, rigorous formulas are given for calculating the corresponding probabilities from the wave function when those probabilities may be consistently defined, thus replacing earlier heuristics for interpreting the wave function of the universe with explicit constructions. It is shown according to a rigorously formulated standard, and in a quantum-mechanically consistent way, that in this quantization these models are generically singular. Independent of the choice of state we show that the probability for these Wheeler-DeWitt quantum universes to ever encounter a singularity is unity. In addition, the relation between histories formulations of quantum theory and relational Dirac observables is clarified.
120825479
The area of isodensity contours in cosmological models and galaxy surveys
La statistique des croisements de contours est definie comme le nombre moyen de fois par unite de longueur qu'une ligne droite tracee au travers du champ de densite traverse un contour donne. Cette statistique est proportionnelle a l'aire de la surface du contour. Cette methode est appliquee a des modeles de champs de densite et a des echantillons lisses de galaxies
120988952
BRANCH WAVE FUNCTIONS FOR QUASI-CLASSICAL HOMOGENEOUS UNIVERSES
122055439
Consistent probabilities in sLQC
We describe a complete, coherent framework within which probabilities may be consistently extracted from amplitudes for quantum histories in loop quantum cosmology. The decoherence functional is constructed for a loop quantization of a flat Friedmann-Lemaǐtre-Robertson-Walker cosmological model, thereby permitting consistent quantum predictions to be made in a mathematically precise model of quantum cosmology. Consistent families of quantum histories are exhibited. Singularity avoidance by generic quantum states in loop-quantized models is contrasted with the failure of parallel Wheeler-DeWitt-quantized universes to avoid the big-bang singularity. It is shown that all loop quantum states approach arbitrarily large volume Wheeler-DeWitt states in both the asymptotic "past" and "future" of emergent time. The critical role played by decoherence of histories in these predictions is illustrated.
182462112
Deadtime of SDC Straw Detectors