Quantum Cosmology

We give an introduction into quantum cosmology with emphasis on its conceptual parts. After a general motivation we review the formalism of canonical quantum gravity on which discussions of quantum cosmology are usually based. We then present the minisuperspace Wheeler--DeWitt equation and elaborate on the problem of time, the imposition of boundary conditions, the semiclassical approximation, the origin of irreversibility, and singularity avoidance. Restriction is made to quantum geometrodynamics; loop quantum gravity and string theory are discussed in other contributions to this volume.Comment: 29 pages, 9 figures, contribution to "Beyond the Big Bang", ed. by R. Vaas (Springer 2008); typos corrected, reference adde

The Water Monomer on the Basal Plane of Ice Iₕ: An Effective Pair, Central Force Potential Model of the Static Interaction

The H2O-H2O intermolecular central force potential of Lemberg and Stillinger is used to obtain optimal binding energy surfaces, vibrational frequencies, and bonding configurations of an adsorbed water monomer on a model basal plane of ice Ih. The monomer interacts (pairwise) with 50 molecules arranged in two layers of the unrelaxed bulk ice lattice. The results of calculations for three model surface sites of differing proton arrangement indicate the existence of diffusion barriers of the order of 2.5 kcal/mole and optimal monomer bonding sites at about 9 kcal/mole with nonepitaxial characteristics. Perspective computer-drawn plots of the optimal monomer binding energy surfaces and the center of mass height of the monomer over each of the three sites are shown. Similar diagrams showing the variations in the monomer dipole orientation along walks across the sites are also presented. Mean residence times and mean path lengths of the monomer diffusing over the model ice surface are estimated from the monomer vibrational modes and the estimated average diffusion barriers and binding energies. A sample diffusion path is discussed

Quantum cosmology with big-brake singularity

We investigate a cosmological model with a big-brake singularity in the future: while the first time derivative of the scale factor goes to zero, its second time derivative tends to minus infinity. Although we also discuss the classical version of the model in some detail, our main interest lies in its quantization. We formulate the Wheeler-DeWitt equation and derive solutions describing wave packets. We show that all such solutions vanish in the region of the classical singularity, a behaviour which we interpret as singularity avoidance. We then discuss the same situation in loop quantum cosmology. While this leads to a different factor ordering, the singularity is there avoided, too.Comment: 24 pages, 7 figures, figures improved, references added, conceptual clarifications include

The Water Monomer on the Prism Face of Ice and above a Four Layer Ice Basal Face Ledge: An Effective Pair Potential Model

A previous study of the water monomer on the basal faces of ice is extended to consider the interaction of the water molecule with a rigid prism face of ice and with an ice basal face ledge. The effective central force H2O-H2O potentials of Stillinger and Rahman are used to generate maximal binding energy surfaces for the H2O adsorbed on the sample substrates. The results indicate that the prism face of ice binds the water molecule more strongly than the basal faces, and the step on the basal face serves to expose high binding sites on the prism face and multiple bonding configurations at the base of the ledge. Bonding on all the substrates is preferred at sites not directly above water molecules in the first or second layer. Average maximal binding energies on the prism and ledge surfaces are 9 kcal/mol compared to a value of 8 kcal/mol on the (unpolarized) basal face. Optimal bonding configuration for the adsorbed water moment are also presented. Barriers to diffusion between maximal binding sites are 2.5 and 3.0 kcal/mol on the basal and prism faces, respectively

Quantum phantom cosmology

We apply the formalism of quantum cosmology to models containing a phantom field. Three models are discussed explicitly: a toy model, a model with an exponential phantom potential, and a model with phantom field accompanied by a negative cosmological constant. In all these cases we calculate the classical trajectories in configuration space and give solutions to the Wheeler-DeWitt equation in quantum cosmology. In the cases of the toy model and the model with exponential potential we are able to solve the Wheeler-DeWitt equation exactly. For comparison, we also give the corresponding solutions for an ordinary scalar field. We discuss in particular the behaviour of wave packets in minisuperspace. For the phantom field these packets disperse in the region that corresponds to the Big Rip singularity. This thus constitutes a genuine quantum region at large scales, described by a regular solution of the Wheeler-DeWitt equation. For the ordinary scalar field, the Big-Bang singularity is avoided. Some remarks on the arrow of time in phantom models as well as on the relation of phantom models to loop quantum cosmology are given.Comment: 21 pages, 6 figure

The intravascular volume effect of Ringer's lactate is below 20%: a prospective study in humans

Introduction: Isotonic crystalloids play a central role in perioperative fluid management. Isooncotic preparations of colloids (for example, human albumin or hydroxyethyl starch) remain nearly completely intravascular when infused to compensate for acute blood losses. Recent data were interpreted to indicate a comparable intravascular volume effect for crystalloids, challenging the occasionally suggested advantage of using colloids to treat hypovolemia. General physiological knowledge and clinical experience, however, suggest otherwise. Methods: In a prospective study, double-tracer blood volume measurements were performed before and after intended normovolemic hemodilution in ten female adults, simultaneously substituting the three-fold amount of withdrawn blood with Ringer's lactate. Any originated deficits were substituted with half the volume of 20% human albumin, followed by a further assessment of blood volume. To assess significance between the measurements, repeated measures analysis of variance (ANOVA) according to Fisher were performed. If significant results were shown, paired t tests (according to Student) for the singular measurements were taken. P < 0.05 was considered to be significant. Results: A total of 1,097 +/- 285 ml of whole blood were withdrawn (641 +/- 155 ml/m2 body surface area) and simultaneously replaced by 3,430 +/- 806 ml of Ringer's lactate. All patients showed a significant decrease in blood volume after hemodilution (-459 +/- 185 ml; P < 0.05) that did not involve relevant hemodynamical changes, and a significant increase in interstitial water content (+ 2,157 +/- 606 ml; P < 0.05). The volume effect of Ringer's lactate was 17 +/- 10%. The infusion of 245 +/- 64 ml of 20% human albumin in this situation restored blood volume back to baseline values, the volume effect being 184 +/- 63%. Conclusions: Substitution of isolated intravascular deficits in cardiopulmonary healthy adults with the three-fold amount of Ringer's lactate impedes maintenance of intravascular normovolemia. The main side effect was an impressive interstitial fluid accumulation, which was partly restored by the intravenous infusion of 20% human albumin. We recommend to substitute the five-fold amount of crystalloids or to use an isooncotic preparation in the face of acute bleeding in patients where edema prevention might be advantageous