Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 04/05 Archiv

Multi-wavelength large-scale surveys are currently exploring the Universe and establishing the cosmological scenario with extraordinary accuracy. There has been recently a significant theoretical and observational progress in efforts to use clusters of galaxies as probes of cosmology and to test the physics of structure formation. Galaxy clusters are the most massive gravitationally bound systems in the Universe, which trace the evolution of the large-scale structure. Their number density and distribution are highly sensitive to the underlying cosmological model. The constraints on cosmological parameters which result from observations of galaxy clusters are complementary with those from other probes. This dissertation examines the crucial role of clusters of galaxies in confirming the standard model of cosmology, with a Universe dominated by dark matter and dark energy. In particular, we examine the clustering of optically selected galaxy clusters as a useful addition to the common set of cosmological observables, because it extends galaxy clustering analysis to the high-peak, high-bias regime. The clustering of galaxy clusters complements the traditional cluster number counts and observable-mass relation analyses, significantly improving their constraining power by breaking existing calibration degeneracies. We begin by introducing the fundamental principles at the base of the concordance cosmological model and the main observational evidence that support it. We then describe the main properties of galaxy clusters and their contribution as cosmological probes. We then present the theoretical framework of galaxy clusters number counts and power spectrum. We revise the formulation and calibration of the halo mass function, whose high mass tail is populated by galaxy clusters. In addition to this, we give a prescription for modelling the cluster redshift space power spectrum, including an effective modelling of the weakly non-linear contribution and allowing for an arbitrary photometric redshift smoothing. Some definitions concerning the study of non-Gaussian initial conditions are presented, because clusters can provide constraints on these models. We dedicate a Chapter to the data we use in our analysis, namely the Sloan Digital Sky Survey maxBCG optical catalogue. We describe the data sets we derived from this large sample of clusters and the corresponding error estimates. Specifically, we employ the cluster abundances in richness bins, the weak-lensing mass estimates and the redshift-space power spectrum, with their respective covariance matrices. We also relate the cluster masses to the observable quantity (richness) by means of an empirical scaling relation and quantify its scatter. In the next Chapter we present the results of our Monte Carlo Markov Chain analysis and the cosmological constraints obtained. With the maxBCG sample, we simultaneously constrain cosmological parameters and cross-calibrate the mass-observable relation. We find that the inclusion of the power spectrum typically brings a 50% improvement in the errors on the fluctuation amplitude and the matter density. Constraints on other parameters are also improved, even if less significantly. In addition to the cluster data, we also use the CMB power spectra from WMAP7, which further tighten the confidence regions. We also apply this method to constrain models of the early universe through the amount of primordial non-Gaussianity of the initial density perturbations (local type) obtaining consistent results with the latest constraints. In the last Chapter, we introduce some preliminary calculations on the cross-correlation between clusters and galaxies, which can provide additional constraining power on cosmological models. In conclusion, we summarise our main achievements and suggest possible future developments of research.

In dieser Arbeit berichten wir über die Beobachtung der dielektrischen Laserbeschleunigung nichtrelativistischer Elektronen mithilfe des inversen Smith-Purcell Effekts bei optischen Wellenlängen. Wenn die Phasengeschwindigkeit von evaneszenten Wellen nahe periodischer Gitterstrukturen mit der Elektronengeschwindigkeit übereinstimmt, kann eine vorwärtsgerichtete elektrische Feldkomponente das Elektron kontinuierlich beschleunigen. Dieser Effekt tritt jedoch nur im Nahfeld passender photonischer Strukturen auf, d.h., dass der Elektronenstrahl die Struktur in Abständen, die kleiner als die Wellenlänge sind, passieren muss. Für die Beschleunigung nichtrelativistischer 28keV Elektronen verwenden wir die dritte Raumharmonische eines Quarzgitters, die mittels Lichtpulsen eines Titan-Saphir-Oszillators angeregt wird. Wir messen einen maximalen Energiegewinn von 280eV, was einem Beschleunigungsgradienten von 25MeV/m entspricht. Dieser Wert ist vergleichbar mit dem Gradienten heutiger Radiofrequenz-Linearbeschleuniger. Um diese Beschleunigung zu erfahren, passieren die Elektronen die Gitteroberfläche in einem Abstand von weniger als 100nm. Im Rahmen dieser Arbeit beschreiben wir die Theorie der Elektronenbeschleunigung im Nahfeld von Gitterstrukturen und diskutieren Simulationsergebnisse zu dieser dielektrischen Laserbeschleunigung. Unsere Messergebnisse stimmen sehr gut mit den Simulationen überein und bestätigen deshalb die direkte Beschleunigung im Lichtfeld. Zusätzlich diskutieren wir die Elektronenbeschleunigung in Doppelgitterstrukturen, das Dephasieren nichtrelativistischer Elektronen, sowie den Raumladungseffekt, der den Spitzenstrahlstrom in diesen neuartigen, auf Mikrostrukturen basierenden Beschleunigern begrenzt. Die hier verwendeten photonischen Gitterstrukturen können direkt aneinandergereiht werden und erfüllen damit die Voraussetzung für skalierbare Linearbeschleuniger. Außerdem sind unsere Strukturen kompatibel mit den Mikrostrukturen, an denen die dielektrische Laserbeschleunigung relativistischer Elektronen zeitgleich durch unsere Kollegen in Stanford demonstriert wurde. Das Potenzial dielektrischer Laserbeschleuniger liegt in dem bis zu zwei Größenordnungen höheren Beschleunigungsgradienten verglichen mit konventionellen Beschleunigereinrichtungen, was sich letztendlich auf die größere Zerstörschwelle dielektrischer Materialien bei optischen Wellenlängen im Vergleich zu Metallen im Radio- und Mikrowellenbereich zurückführen lässt, die eine erhöhte Oberflächenspannungsfestigkeit zur Folge hat. Dieser erhöhte Beschleunigungsgradient könnte den Bau von deutlich kompakteren und kostengünstigeren Beschleunigern erlauben. Wir geben einen Ausblick auf den möglichen Aufbau solcher zukünftiger optischen Beschleuniger und auf deren potentiellen Anwendungen in kompakten Freie-Elektronen-Lasern.

In the first part of this thesis, basic mathematical and physical concepts are introduced. The notion of a Lie algebroid is reviewed in detail and we explain the generalization of differential geometric structures when the tangent bundle is replaced by a Lie algebroid. In addition, Lie bi-algebroids and Courant algebroids are defined. This branch of mathematics finds its application in deformation quantization, which in string theory is the dynamics of open strings in the presence of a background B-field. We explain how the Moyal-Weyl star product arises for constant background fields and how this can be generalized to arbitrary backgrounds and non-associative products. Non-commutative or even non-associative spaces are expected to play a role also in closed string theory: Starting with a compactification on toroidal backgrounds with non-trivial H-flux, T-duality leads on the one hand to configurations with geometric f-flux, but on the other hand to spaces which are only locally geometric in case of Q-flux, or even non-commutative or non-associative in case of the R-flux. We describe the action of T-duality in detail and review the motivation and structure of non-geometric fluxes. It will turn out, that in the local description of non-geometric backgrounds, a bi-vector $\beta$ is more appropriate than the original B-field. Based on these foundations, we will describe our results in the second part. On the world-sheet level, we will analyse closed string theory with flat background and constant H-flux. The correct choice of left- and right-moving currents allows for a conformal field theory description of this background up to linear order in the H-flux. It is possible to define tachyon vertex operators and T-duality is implemented as a simple reflection of the right-moving sector. In analogy to the open string case, correlation functions allow to extract information on the algebra of observables on the target space. We observe a non-vanishing three-coordinate correlator and after the application of an odd number of T-dualities, we are able to extract a three-product which has a structure similar to the Moyal-Weyl product. We then focus on the target space and the local structure of the H-,f-,Q- and R-fluxes. An algebra based on vector fields is proposed, whose structure functions are given by the fluxes and Jacobi-identities allow for the computation of Bianchi-identities. Based on the latter, we give a proof for a special Courant algebroid structure on the generalized tangent bundle $TM \oplus T^*M$, where the fluxes are realized by the commutation relations of a basis of sections. As was reviewed in the first part of this work, in the description of non-geometric Q- and R-fluxes, the B-field gets replaced by a bi-vector $\beta$, which is supposed to serve as the dual object to B under T-duality. A natural question is about the existence of a differential geometric framework allowing the construction of actions manifestly invariant under coordinate- and gauge transformations, which couple the $\beta$-field to gravity. It turns out that we have to use the language of Lie algebroids to extend differential geometry from the tangent bundle of the target space to its cotangent bundle, equipped with a twisted version of the Koszul-Schouten bracket, to answer this question positively. This construction enables us to formulate covariant derivatives, torsion, curvature and gauge symmetries and culminates in an Einstein-Hilbert action for the metric and $\beta$-field. We observe that this action is related to standard bosonic low energy string theory by a field redefinition, which was discovered by Seiberg and Witten and which we described in detail in the first part. Furthermore it turns out, that the whole construction can be extended to higher order corrections in $\alpha'$ and to the type IIA superstring. We conclude by giving an outlook on future directions. After clarifying the relation of Lie algebroids to non-geometry, we speculate about the application of Lie algebroid constructions to supersymmetry and the extension to the case of Filippov three-algebroids, which could play a role in M-theory.

In dieser Arbeit wird eine Messung der Top-Quark Masse im vollhadronischen Top-Antitop Zerfallskanal präsentiert. Die Messung basiert auf Daten des ATLAS Detektors aus Proton-Proton Kollisionen, welche am LHC bei einer Schwerpunktsenergie von 7 TeV durchgeführt wurde. Der Datensatz wurde im Jahr 2011 aufgezeichnet und entspricht einer integrierten Luminosität von 4.7 fb^-1. Die Messung der Top-Quark Masse erfolgt mittels einer Template-Technik, wobei die sogenannte R_3/2 Variable als Top-Quark-Massen sensitive Größe benutzt wird. Die R_3/2 Variable errechnet sich hierbei aus dem Verhältnis der invarianten Massen des hadronisch zerfallenden Top-Quarks und W-Bosons. Die Zuordnung von Jets zu den jeweiligen Top-Antitop Zerfalls-Partonen ergibt sich anhand einer Wahrscheinlichkeitsvorhersage, welche die kinematischen Eigenschaften der Jets berücksichtigt. Der Multijet Untergrund des vollhadronischen Top-Antitop Signals wird mittels Daten abgeschätzt, wodurch eine präzise Vorhersage der kinematischen Verteilungen von Untergrund-Ereignissen ermöglicht wird. Die Messung der Top-Quark Masse ergibt m_top = 175.1 +- 1.4 (stat.) +- 1.8 (syst.) GeV/c^2, wobei die dominanten Beiträge zur systematischen Unsicherheit von der Jet-Energie-Skala sowie von der b-Jet Energie-Skala stammen.

This thesis discusses several aspects of string field theory. The first issue is bosonic open-closed string field theory and its associated algebraic structure -- the quantum open-closed homotopy algebra. We describe the quantum open-closed homotopy algebra in the framework of homotopy involutive Lie bialgebras, as a morphism from the loop homotopy Lie algebra of closed string to the involutive Lie bialgebra on the Hochschild complex of open strings. The formulation of the classical/quantum open-closed homotopy algebra in terms of a morphism from the closed string algebra to the open string Hochschild complex reveals deformation properties of closed strings on open string field theory. In particular, we show that inequivalent classical open string field theories are parametrized by closed string backgrounds up to gauge transformations. At the quantum level the correspondence is obstructed, but for other realizations such as the topological string, a non-trivial correspondence persists. Furthermore, we proof the decomposition theorem for the loop homotopy Lie algebra of closed string field theory, which implies uniqueness of closed string field theory on a fixed conformal background. Second, the construction of string field theory can be rephrased in terms of operads. In particular, we show that the formulation of string field theory splits into two parts: The first part is based solely on the moduli space of world sheets and ensures that the perturbative string amplitudes are recovered via Feynman rules. The second part requires a choice of background and determines the real string field theory vertices. Each of these parts can be described equivalently as a morphism between appropriate cyclic and modular operads, at the classical and quantum level respectively. The algebraic structure of string field theory is then encoded in the composition of these two morphisms. Finally, we outline the construction of type II superstring field theory. Specific features of the superstring are the appearance of Ramond punctures and the picture changing operators. The sewing in the Ramond sector requires an additional constraint on the state space of the world sheet conformal field theory, such that the associated symplectic structure is non-degenerate, at least on-shell. Moreover, we formulate an appropriate minimal area metric problem for type II world sheets, which can be utilized to sketch the construction of a consistent set of geometric vertices. The algebraic structure of type II superstring field theory is that of a $\mathcal{N}=1$ loop homotopy Lie algebra at the quantum level, and that of a $\mathcal{N}=1$ homotopy Lie algebra at the classical level.