Open FRW model in Loop Quantum Cosmology

Open FRW model in Loop Quantum Cosmology is under consideration. The left and right invariant vector fields and holonomies along them are studied. It is shown that in the hyperbolic geometry of $k=-1$ it is possible to construct a suitable loop which provides us with quantum scalar constraint originally introduced by Vandersloot. The quantum scalar constraint operator with negative cosmological constant is proved to be essentially self-adjoint.Comment: 12 pages, no figures, late

Eber und Börge im Vergleich – Auswirkungen der Kastration auf agonistisches und sexuell motiviertes Verhalten unter ökologischen Haltungsbedingungen

Nach dem Verbot der betäubungslosen Ferkelkastration nach VO (EG) 889 (2008) zum 01.01.2012 stellt die Ebermast eine mögliche Alternative für die ökologische Schweinefleischerzeugung dar. Im Rahmen des Projektes „Ebermast im Verbund: Entwicklung eines Konzepts für die Produktion, Schlachtung, Verarbeitung und Vermarktung ökologisch erzeugter Eber entlang der Wertschöpfungskette“ ist es ein Ziel, das Ausmaß möglichen unerwünschten Verhaltens, wie agonistische Interaktionen und Aufreitverhalten der Eber, mit dem von Börgen unter praxisüblichen ökologischen Haltungsbedingungen zu vergleichen und wichtige Einflussfaktoren hierauf zu identifizieren. Auch mögliche Verletzungsfolgen sollen einbezogen werden. Aus einer Zwischenauswertung werden hier erste Ergebnisse zum Ausmaß des genannten Verhaltens und der Verletzungsfolgen vorgestellt. 9 Gruppen Eber und 7 Gruppen Börge wurden mit einem Lebendgewicht von etwa 80 kg auf vier ökologischen Praxisbetrieben beobachtet. Agonistische Interaktionen (Kopfschlagen, Beißen, Kampf und Besteigen ohne sexuelle Motivation) und Besteigen mit sexueller Motivation wurden mittels kontinuierlicher Verhaltenszählung (continuous behaviour sampling) jeweils über die ersten 15 Minuten einer jeden Lichtstunde von zusammenhängenden 48h-Aufnahmen ausgewertet. Zum selben Zeitpunkt wurden zusätzlich die Verletzungen bei den 109 Ebern und 91 Börgen gezählt. Eber zeigten bezüglich aller erhobener Verhaltensparameter gegenüber den Börgen signifikant höhere Häufigkeiten bzw. Dauern. Dagegen konnten hinsichtlich der Verletzungsscores zwischen Ebern und Börgen keine signifikanten Unterschiede festgestellt werden. Die Untersuchung wird fortgesetzt

Effective dynamics of the closed loop quantum cosmology

In this paper we study dynamics of the closed FRW model with holonomy corrections coming from loop quantum cosmology. We consider models with a scalar field and cosmological constant. In case of the models with cosmological constant and free scalar field, dynamics reduce to 2D system and analysis of solutions simplify. If only free scalar field is included then universe undergoes non-singular oscillations. For the model with cosmological constant, different behaviours are obtained depending on the value of $\Lambda$. If the value of $\Lambda$ is sufficiently small, bouncing solutions with asymptotic de Sitter stages are obtained. However if the value of $\Lambda$ exceeds critical value $\Lambda_{\text{c}} =\frac{\sqrt{3}m^2_{\text{Pl}}}{2\pi\gamma^3} \simeq 21 m^2_{\text{Pl}}$ then solutions become oscillatory. Subsequently we study models with a massive scalar field. We find that this model possess generic inflationary attractors. In particular field, initially situated in the bottom of the potential, is driven up during the phase of quantum bounce. This subsequently leads to the phase of inflation. Finally we find that, comparing with the flat case, effects of curvature do not change qualitatively dynamics close to the phase of bounce. Possible effects of inverse volume corrections are also briefly discussed.Comment: 18 pages, 11 figure

The status of Quantum Geometry in the dynamical sector of Loop Quantum Cosmology

This letter is motivated by the recent papers by Dittrich and Thiemann and, respectively, by Rovelli discussing the status of Quantum Geometry in the dynamical sector of Loop Quantum Gravity. Since the papers consider model examples, we also study the issue in the case of an example, namely on the Loop Quantum Cosmology model of space-isotropic universe. We derive the Rovelli-Thiemann-Ditrich partial observables corresponding to the quantum geometry operators of LQC in both Hilbert spaces: the kinematical one and, respectively, the physical Hilbert space of solutions to the quantum constraints. We find, that Quantum Geometry can be used to characterize the physical solutions, and the operators of quantum geometry preserve many of their kinematical properties.Comment: Latex, 12 page

Beyond deficiency:Potential benefits of increased intakesof vitamin K for bone and vascular health

Vitamin K is wellknown for its role in the synthesisof a number of blood coagulationfactors.During recent years vitaminK-dependent proteins werediscovered to be of vital importancefor bone and vascular health.Recommendations for dietary vitaminK intake have been made onthe basis of the hepatic requirementsfor the synthesis of bloodcoagulation factors.Accumulatingevidence suggests that the requirementsfor other functions thanblood coagulation may be higher.This paper is the result of a closedworkshop (Paris,November 2002)in which a number of Europeanvitamin K experts reviewed theavailable data and formulated theirstandpoint with respect to recommendeddietary vitamin K intakeand the use of vitamin K-containingsupplements

Transcending Big Bang in Loop Quantum Cosmology: Recent Advances

We discuss the way non-perturbative quantization of cosmological spacetimes in loop quantum cosmology provides insights on the physics of Planck scale and the resolution of big bang singularity. In recent years, rigorous examination of mathematical and physical aspects of the quantum theory has led to a consistent quantization which is consistent and physically viable and some early ideas have been ruled out. The latter include so called `physical effects' originating from modifications to inverse scale factors in the flat models. The singularity resolution is understood to originate from the non-local nature of curvature in the quantum theory and the underlying polymer representation. Using an exactly solvable model various insights have been gained. The model predicts a generic occurrence of bounce for states in the physical Hilbert space and a supremum for the spectrum of the energy density operator. It also provides answers to the growth of fluctuations, showing that semi-classicality is preserved to an amazing degree across the bounce.Comment: Invited plenary talk at the Sixth International Conference on Gravitation and Cosmology, IUCAA (Pune). 13 pages, 3 figure

Non-singular Universes a la Palatini

It has recently been shown that f(R) theories formulated in the Palatini variational formalism are able to avoid the big bang singularity yielding instead a bouncing solution. The mechanism responsible for this behavior is similar to that observed in the effective dynamics of loop quantum cosmology and an f(R) theory exactly reproducing that dynamics has been found. I will show here that considering more general actions, with quadratic contributions of the Ricci tensor, results in a much richer phenomenology that yields bouncing solutions even in anisotropic (Bianchi I) scenarios. Some implications of these results are discussed.Comment: 4 pages, no figures. Contribution to the Spanish Relativity Meeting (ERE2010), 6-10 Sept. Granada, Spai

Closed FRW model in Loop Quantum Cosmology

The basic idea of the LQC applies to every spatially homogeneous cosmological model, however only the spatially flat (so called $k=0$) case has been understood in detail in the literature thus far. In the closed (so called: k=1) case certain technical difficulties have been the obstacle that stopped the development. In this work the difficulties are overcome, and a new LQC model of the spatially closed, homogeneous, isotropic universe is constructed. The topology of the spacelike section of the universe is assumed to be that of SU(2) or SO(3). Surprisingly, according to the results achieved in this work, the two cases can be distinguished from each other just by the local properties of the quantum geometry of the universe. The quantum hamiltonian operator of the gravitational field takes the form of a difference operator, where the elementary step is the quantum of the 3-volume derived in the flat case by Ashtekar, Pawlowski and Singh. The mathematical properties of the operator are studied: it is essentially self-adjoint, bounded from above by 0, the 0 itself is not an eigenvalue, the eigenvectors form a basis. An estimate on the dimension of the spectral projection on any finite interval is provided.Comment: 19 pages, latex, no figures, high quality, nea

Classical Setting and Effective Dynamics for Spinfoam Cosmology

We explore how to extract effective dynamics from loop quantum gravity and spinfoams truncated to a finite fixed graph, with the hope of modeling symmetry-reduced gravitational systems. We particularize our study to the 2-vertex graph with N links. We describe the canonical data using the recent formulation of the phase space in terms of spinors, and implement a symmetry-reduction to the homogeneous and isotropic sector. From the canonical point of view, we construct a consistent Hamiltonian for the model and discuss its relation with Friedmann-Robertson-Walker cosmologies. Then, we analyze the dynamics from the spinfoam approach. We compute exactly the transition amplitude between initial and final coherent spin networks states with support on the 2-vertex graph, for the choice of the simplest two-complex (with a single space-time vertex). The transition amplitude verifies an exact differential equation that agrees with the Hamiltonian constructed previously. Thus, in our simple setting we clarify the link between the canonical and the covariant formalisms.Comment: 38 pages, v2: Link with discretized loop quantum gravity made explicit and emphasize