Imaging the Cosmic Matter Distribution using Gravitational Lensing of Pregalactic HI

21-cm emission from neutral hydrogen during and before the epoch of cosmic reionisation is gravitationally lensed by material at all lower redshifts. Low-frequency radio observations of this emission can be used to reconstruct the projected mass distribution of foreground material, both light and dark. We compare the potential imaging capabilities of such 21-cm lensing with those of future galaxy lensing surveys. We use the Millennium Simulation to simulate large-area maps of the lensing convergence with the noise, resolution and redshift-weighting achievable with a variety of idealised observation programmes. We find that the signal-to-noise of 21-cm lens maps can far exceed that of any map made using galaxy lensing. If the irreducible noise limit can be reached with a sufficiently large radio telescope, the projected convergence map provides a high-fidelity image of the true matter distribution, allowing the dark matter halos of individual galaxies to be viewed directly, and giving a wealth of statistical and morphological information about the relative distributions of mass and light. For instrumental designs like that planned for the Square Kilometer Array (SKA), high-fidelity mass imaging may be possible near the resolution limit of the core array of the telescope.Comment: version accepted for publication in MNRAS (reduced-resolution figures

Quantum Kaleidoscopes and Bell's theorem

A quantum kaleidoscope is defined as a set of observables, or states, consisting of many different subsets that provide closely related proofs of the Bell-Kochen-Specker (BKS) and Bell nonlocality theorems. The kaleidoscopes prove the BKS theorem through a simple parity argument, which also doubles as a proof of Bell's nonlocality theorem if use is made of the right sort of entanglement. Three closely related kaleidoscopes are introduced and discussed in this paper: a 15-observable kaleidoscope, a 24-state kaleidoscope and a 60-state kaleidoscope. The close relationship of these kaleidoscopes to a configuration of 12 points and 16 lines known as Reye's configuration is pointed out. The "rotations" needed to make each kaleidoscope yield all its apparitions are laid out. The 60-state kaleidoscope, whose underlying geometrical structure is that of ten interlinked Reye's configurations (together with their duals), possesses a total of 1120 apparitions that provide proofs of the two Bell theorems. Some applications of these kaleidoscopes to problems in quantum tomography and quantum state estimation are discussed.Comment: Two new references (No. 21 and 22) to related work have been adde

Vortices on Hyperbolic Surfaces

It is shown that abelian Higgs vortices on a hyperbolic surface $M$ can be constructed geometrically from holomorphic maps $f:M \to N$, where $N$ is also a hyperbolic surface. The fields depend on $f$ and on the metrics of $M$ and $N$. The vortex centres are the ramification points, where the derivative of $f$ vanishes. The magnitude of the Higgs field measures the extent to which $f$ is locally an isometry. Witten's construction of vortices on the hyperbolic plane is rederived, and new examples of vortices on compact surfaces and on hyperbolic surfaces of revolution are obtained. The interpretation of these solutions as SO(3)-invariant, self-dual SU(2) Yang--Mills fields on $\R^4$ is also given.Comment: Revised version: new section on four-dimensional interpretation of hyperbolic vortices added

Luminosity distance in Swiss cheese cosmology with randomized voids. II. Magnification probability distributions

We study the fluctuations in luminosity distances due to gravitational lensing by large scale (> 35 Mpc) structures, specifically voids and sheets. We use a simplified "Swiss cheese" model consisting of a \Lambda -CDM Friedman-Robertson-Walker background in which a number of randomly distributed non-overlapping spherical regions are replaced by mass compensating comoving voids, each with a uniform density interior and a thin shell of matter on the surface. We compute the distribution of magnitude shifts using a variant of the method of Holz & Wald (1998), which includes the effect of lensing shear. The standard deviation of this distribution is ~ 0.027 magnitudes and the mean is ~ 0.003 magnitudes for voids of radius 35 Mpc, sources at redshift z_s=1.0, with the voids chosen so that 90% of the mass is on the shell today. The standard deviation varies from 0.005 to 0.06 magnitudes as we vary the void size, source redshift, and fraction of mass on the shells today. If the shell walls are given a finite thickness of ~ 1 Mpc, the standard deviation is reduced to ~ 0.013 magnitudes. This standard deviation due to voids is a factor ~ 3 smaller than that due to galaxy scale structures. We summarize our results in terms of a fitting formula that is accurate to ~ 20%, and also build a simplified analytic model that reproduces our results to within ~ 30%. Our model also allows us to explore the domain of validity of weak lensing theory for voids. We find that for 35 Mpc voids, corrections to the dispersion due to lens-lens coupling are of order ~ 4%, and corrections to due shear are ~ 3%. Finally, we estimate the bias due to source-lens clustering in our model to be negligible

Combining cluster observables and stacked weak lensing to probe dark energy: Self-calibration of systematic uncertainties

We develop a new method of combining cluster observables (number counts and cluster-cluster correlation functions) and stacked weak lensing signals of background galaxy shapes, both of which are available in a wide-field optical imaging survey. Assuming that the clusters have secure redshift estimates, we show that the joint experiment enables a self-calibration of important systematic errors including the source redshift uncertainty and the cluster mass-observable relation, by adopting a single population of background source galaxies for the lensing analysis. It allows us to use the relative strengths of stacked lensing signals at different cluster redshifts for calibrating the source redshift uncertainty, which in turn leads to accurate measurements of the mean cluster mass in each bin. In addition, our formulation of stacked lensing signals in Fourier space simplifies the Fisher matrix calculations, as well as the marginalization over the cluster off-centering effect, the most significant uncertainty in stacked lensing. We show that upcoming wide-field surveys yield stringent constraints on cosmological parameters including dark energy parameters, without any priors on nuisance parameters that model systematic uncertainties. Specifically, the stacked lensing information improves the dark energy FoM by a factor of 4, compared to that from the cluster observables alone. The primordial non-Gaussianity parameter can also be constrained with a level of f_NL~10. In this method, the mean source redshift is well calibrated to an accuracy of 0.1 in redshift, and the mean cluster mass in each bin to 5-10% accuracies, which demonstrates the success of the self-calibration of systematic uncertainties from the joint experiment. (Abridged)Comment: 29 pages, 17 figures, 6 tables, accepted for publication in Phys. Rev.

Evidence of fNIRS-based prefrontal cortex hypoactivity in obesity and binge-eating disorder

Obesity (OB) and associated binge-eating disorder (BED) show increased impulsivity and emotional dysregulation. Albeit well-established in neuropsychiatric research, functional near-infrared spectroscopy (fNIRS) has rarely been used to study OB and BED. Here, we investigated fNIRS-based food-specific brain signalling, its association with impulsivity and emotional dysregulation, and the temporal variability in individuals with OB with and without BED compared to an age- and sex-stratified normal weight (NW) group. Prefrontal cortex (PFC) responses were recorded in individuals with OB (n = 15), OB + BED (n = 13), and NW (n = 12) in a passive viewing and a response inhibition task. Impulsivity and emotional dysregulation were self-reported; anthropometrics were objectively measured. The OB and NW groups were measured twice 7 days apart. Relative to the NW group, the OB and OB + BED groups showed PFC hyporesponsivity across tasks, whereas there were few significant differences between the OB and OB + BED groups. Greater levels of impulsivity were significantly associated with stronger PFC responses, while more emotional dysregulation was significantly associated with lower PFC responses. Temporal differences were found in the left orbitofrontal cortex responses, yet in opposite directions in the OB and NW groups. This study demonstrated diminished fNIRS-based PFC responses across OB phenotypes relative to a NW group. The association between impulsivity, emotional dysregulation, and PFC hypoactivity supports the assumption that BED constitutes a specific OB phenotype

Structure and dynamics of topological defects in a glassy liquid on a negatively curved manifold

We study the low-temperature regime of an atomic liquid on the hyperbolic plane by means of molecular dynamics simulation and we compare the results to a continuum theory of defects in a negatively curved hexagonal background. In agreement with the theory and previous results on positively curved (spherical) surfaces, we find that the atomic configurations consist of isolated defect structures, dubbed "grain boundary scars", that form around an irreducible density of curvature-induced disclinations in an otherwise hexagonal background. We investigate the structure and the dynamics of these grain boundary scars

Defects and boundary layers in non-Euclidean plates

We investigate the behavior of non-Euclidean plates with constant negative Gaussian curvature using the F\"oppl-von K\'arm\'an reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic profile. We prove rigorous upper and lower bounds for the elastic energy that scales like the thickness squared. In particular we show that are only two types of global minimizers -- deformations that remain flat and saddle shaped deformations with isolated regions of stretching near the edge of the annulus. We also show that there exist local minimizers with a periodic profile that have additional boundary layers near their lines of inflection. These additional boundary layers are a new phenomenon in thin elastic sheets and are necessary to regularize jump discontinuities in the azimuthal curvature across lines of inflection. We rigorously derive scaling laws for the width of these boundary layers as a function of the thickness of the sheet

Ray-tracing through the Millennium Simulation: Born corrections and lens-lens coupling in cosmic shear and galaxy-galaxy lensing

(abridged) We study the accuracy of various approximations to cosmic shear and weak galaxy-galaxy lensing and investigate effects of Born corrections and lens-lens coupling. We use ray-tracing through the Millennium Simulation to calculate various cosmic-shear and galaxy-galaxy-lensing statistics. We compare the results from ray-tracing to semi-analytic predictions. We find: (i) The linear approximation provides an excellent fit to cosmic-shear power spectra as long as the actual matter power spectrum is used as input. Common fitting formulae, however, strongly underestimate the cosmic-shear power spectra. Halo models provide a better fit to cosmic shear-power spectra, but there are still noticeable deviations. (ii) Cosmic-shear B-modes induced by Born corrections and lens-lens coupling are at least three orders of magnitude smaller than cosmic-shear E-modes. Semi-analytic extensions to the linear approximation predict the right order of magnitude for the B-mode. Compared to the ray-tracing results, however, the semi-analytic predictions may differ by a factor two on small scales and also show a different scale dependence. (iii) The linear approximation may under- or overestimate the galaxy-galaxy-lensing shear signal by several percent due to the neglect of magnification bias, which may lead to a correlation between the shear and the observed number density of lenses. We conclude: (i) Current semi-analytic models need to be improved in order to match the degree of statistical accuracy expected for future weak-lensing surveys. (ii) Shear B-modes induced by corrections to the linear approximation are not important for future cosmic-shear surveys. (iii) Magnification bias can be important for galaxy-galaxy-lensing surveys.Comment: version taking comments into accoun