Power spectra from an inflaton coupled to the Gauss-Bonnet term

We consider power-law inflation with a Gauss-Bonnet correction inspired by string theory. We analyze the stability of cosmological perturbations and obtain the allowed parameter space. We find that for GB-dominated inflation ultra-violet instabilities of either scalar or tensor perturbations show up on small scales. The Gauss-Bonnet correction with a positive (or negative) coupling may lead to a reduction (or enhancement) of the tensor-to-scalar ratio in the potential-dominated case. We place tight constraints on the model parameters by making use of the WMAP 5-year data.Comment: 5 pages, 4 figures, RevTeX, references added, published versio

On the Nature and Location of the Microlenses

This paper uses the caustic crossing events in the microlens data sets to explore the nature and location of the lenses. We conclude that the large majority of lenses, whether they are luminous or dark, are likely to be binaries. Further, we demonstrate that blending is an important feature of all the data sets. An additional interpretation suggested by the data, that the caustic crossing events along the directions to the Magellanic Clouds are due to lenses located in the Clouds, implies that most of the LMC/SMC events to date are due to lenses in the Magellanic Clouds. All of these conclusions can be tested. If they are correct, a large fraction of lenses along the direction to the LMC may be ordinary stellar binary systems, just as are the majority of the lenses along the direction to the Bulge. Thus, a better understanding of the larger-than-anticipated value derived for the Bulge optical depth may allow us to better interpret the large value derived for the optical depth to the LMC. Indeed, binarity and blending in the data sets may illuminate connections among several other puzzles: the dearth of binary-source light curves, the dearth of non-caustic-crossing perturbed binary-lens events, and the dearth of obviously blended point-lens events.Comment: 15 pages, 2 figures. Submitted to the Astrophysical Journal Letters, 4 January 199

Characterizations of Morse quasi-geodesics via superlinear divergence and sublinear contraction

We introduce and begin a systematic study of sublinearly contracting projections. We give two characterizations of Morse quasi-geodesics in an arbitrary geodesic metric space. One is that they are sublinearly contracting; the other is that they have completely superlinear divergence. We give a further characterization of sublinearly contracting projections in terms of projections of geodesic segments.Comment: 24 pages, 5 figures. v2: 22 pages, 5 figures. Correction in proof of Thm 7.1. Proof of Prop 4.2 revised for improved clarity. Other minor changes per referee comments. To appear in Documenta Mathematic

Negative curvature in graphical small cancellation groups

We use the interplay between combinatorial and coarse geometric versions of negative curvature to investigate the geometry of infinitely presented graphical $Gr'(1/6)$ small cancellation groups. In particular, we characterize their 'contracting geodesics', which should be thought of as the geodesics that behave hyperbolically. We show that every degree of contraction can be achieved by a geodesic in a finitely generated group. We construct the first example of a finitely generated group $G$ containing an element $g$ that is strongly contracting with respect to one finite generating set of $G$ and not strongly contracting with respect to another. In the case of classical $C'(1/6)$ small cancellation groups we give complete characterizations of geodesics that are Morse and that are strongly contracting. We show that many graphical $Gr'(1/6)$ small cancellation groups contain strongly contracting elements and, in particular, are growth tight. We construct uncountably many quasi-isometry classes of finitely generated, torsion-free groups in which every maximal cyclic subgroup is hyperbolically embedded. These are the first examples of this kind that are not subgroups of hyperbolic groups. In the course of our analysis we show that if the defining graph of a graphical $Gr'(1/6)$ small cancellation group has finite components, then the elements of the group have translation lengths that are rational and bounded away from zero.Comment: 40 pages, 14 figures, v2: improved introduction, updated statement of Theorem 4.4, v3: new title (previously: "Contracting geodesics in infinitely presented graphical small cancellation groups"), minor changes, to appear in Groups, Geometry, and Dynamic

Lattice simulation of a center symmetric three-dimensional effective theory for SU(2) Yang-Mills

We perform simulations of an effective theory of SU(2) Wilson lines in three dimensions. Our action includes a kinetic term, the one-loop perturbative potential for the Wilson line, a non-perturbative "fuzzy-bag" contribution and spatial gauge fields. We determine the phase diagram of the theory and confirm that, at moderately weak coupling, the non-perturbative term leads to eigenvalue repulsion in a finite region above the deconfining phase transition.Comment: To appear in the proceedings of "Strong and Electroweak Matter", Amsterdam, the Netherlands, August 26-29, Nucl. Phys. A, in prin

Terrestrial Planet Formation in Extra-Solar Planetary Systems

Terrestrial planets form in a series of dynamical steps from the solid component of circumstellar disks. First, km-sized planetesimals form likely via a combination of sticky collisions, turbulent concentration of solids, and gravitational collapse from micron-sized dust grains in the thin disk midplane. Second, planetesimals coalesce to form Moon- to Mars-sized protoplanets, also called "planetary embryos". Finally, full-sized terrestrial planets accrete from protoplanets and planetesimals. This final stage of accretion lasts about 10-100 Myr and is strongly affected by gravitational perturbations from any gas giant planets, which are constrained to form more quickly, during the 1-10 Myr lifetime of the gaseous component of the disk. It is during this final stage that the bulk compositions and volatile (e.g., water) contents of terrestrial planets are set, depending on their feeding zones and the amount of radial mixing that occurs. The main factors that influence terrestrial planet formation are the mass and surface density profile of the disk, and the perturbations from giant planets and binary companions if they exist. Simple accretion models predicts that low-mass stars should form small, dry planets in their habitable zones. The migration of a giant planet through a disk of rocky bodies does not completely impede terrestrial planet growth. Rather, "hot Jupiter" systems are likely to also contain exterior, very water-rich Earth-like planets, and also "hot Earths", very close-in rocky planets. Roughly one third of the known systems of extra-solar (giant) planets could allow a terrestrial planet to form in the habitable zone.Comment: 19 pages, 5 figures. To appear in the proceedings of IAU Symposium 249: Exoplanets: Detection, Formation and Dynamics, held in Suzhou, China, Oct 22-26 200

Tan(beta)-enhanced supersymmetric corrections to the anomalous magnetic moment of the muon

We report on a two-loop supersymmetric contribution to the magnetic moment (g-2)_mu of the muon which is enhanced by two powers of tan(beta). This contribution arises from a shift in the relation between the muon mass and Yukawa coupling and can increase the supersymmetric contribution to (g-2)_mu sizably. As a result, if the currently observed 3 sigma deviation between the experimental and SM theory value of (g-2)_mu is analyzed within the Minimal Supersymmetric Standard Model (MSSM), the derived constraints on the parameter space are modified significantly: If (g-2)_mu is used to determine tan(beta) as a function of the other MSSM parameters, our corrections decrease tan(beta) by roughly 10% for tan(beta)=50.Comment: 4 pages, 1 figur

Dynamics and evaporation of defects in Mott-insulating clusters of boson pairs

Repulsively bound pairs of particles in a lattice governed by the Bose-Hubbard model can form stable incompressible clusters of dimers corresponding to finite-size n=2 Mott insulators. Here we study the dynamics of hole defects in such clusters corresponding to unpaired particles which can resonantly tunnel out of the cluster into the lattice vacuum. Due to bosonic statistics, the unpaired particles have different effective mass inside and outside the cluster, and "evaporation" of hole defects from the cluster boundaries is possible only when their quasi-momenta are within a certain transmission range. We show that quasi-thermalization of hole defects occurs in the presence of catalyzing particle defects which thereby purify the Mott insulating clusters. We study the dynamics of one-dimensional system using analytical techniques and numerically exact t-DMRG simulations. We derive an effective strong-interaction model that enables simulations of the system dynamics for much longer times. We also discuss a more general case of two bosonic species which reduces to the fermionic Hubbard model in the strong interaction limit.Comment: 12 pages, 10 figures, minor update

Analysis of an Ultra-precision Positioning System and Parametrization of Its Structural Model for Error Compensation

Conventional compensation of position errors of machine tools relies only on measured values. Due to this principle it is not always possible to compensate the errors in time, especially dynamic ones. Moreover, the relevant control variables cannot always be measured directly. Thus, this approach proves to be insufficient for high precision applications. In this context, a model-based error prediction allows for minimal position errors. However, ultra-precision applications set high demands for the models' accuracy. This paper presents the design of an accurate and real time-capable structural model of an ultra-precision positioning system. The modeling method for the developed ultra-precision demonstrator is shown and the initial parameter identification is presented. © 2017 The Authors. Published by Elsevier B.V.DFG/FOR/184