Strong lensing optical depths in a \LambdaCDM universe

We investigate strong gravitational lensing in the concordance $\Lambda$CDM cosmology by carrying out ray-tracing along past light cones through the Millennium Simulation, the largest simulation of cosmic structure formation ever carried out. We extend previous ray-tracing methods in order to take full advantage of the large volume and the excellent spatial and mass resolution of the simulation. As a function of source redshift we evaluate the probability that an image will be highly magnified, will be highly elongated or will be one of a set of multiple images. We show that such strong lensing events can almost always be traced to a single dominant lensing object and we study the mass and redshift distribution of these primary lenses. We fit analytic models to the simulated dark halos in order to study how our optical depth measurements are affected by the limited resolution of the simulation and of the lensing planes that we construct from it. We conclude that such effects lead us to underestimate total strong-lensing cross sections by about 15 percent. This is smaller than the effects expected from our neglect of the baryonic components of galaxies. Finally we investigate whether strong lensing is enhanced by material in front of or behind the primary lens. Although strong lensing lines-of-sight are indeed biased towards higher than average mean densities, this additional matter typically contributes only a few percent of the total surface density.Comment: version accepted for publicatio

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

Discriminants, symmetrized graph monomials, and sums of squares

Motivated by the necessities of the invariant theory of binary forms J. J. Sylvester constructed in 1878 for each graph with possible multiple edges but without loops its symmetrized graph monomial which is a polynomial in the vertex labels of the original graph. In the 20-th century this construction was studied by several authors. We pose the question for which graphs this polynomial is a non-negative resp. a sum of squares. This problem is motivated by a recent conjecture of F. Sottile and E. Mukhin on discriminant of the derivative of a univariate polynomial, and an interesting example of P. and A. Lax of a graph with 4 edges whose symmetrized graph monomial is non-negative but not a sum of squares. We present detailed information about symmetrized graph monomials for graphs with four and six edges, obtained by computer calculations

Cosmic Shear Results from the Deep Lens Survey - II: Full Cosmological Parameter Constraints from Tomography

We present a tomographic cosmic shear study from the Deep Lens Survey (DLS), which, providing a limiting magnitude r_{lim}~27 (5 sigma), is designed as a pre-cursor Large Synoptic Survey Telescope (LSST) survey with an emphasis on depth. Using five tomographic redshift bins, we study their auto- and cross-correlations to constrain cosmological parameters. We use a luminosity-dependent nonlinear model to account for the astrophysical systematics originating from intrinsic alignments of galaxy shapes. We find that the cosmological leverage of the DLS is among the highest among existing >10 sq. deg cosmic shear surveys. Combining the DLS tomography with the 9-year results of the Wilkinson Microwave Anisotropy Probe (WMAP9) gives Omega_m=0.293_{-0.014}^{+0.012}, sigma_8=0.833_{-0.018}^{+0.011}, H_0=68.6_{-1.2}^{+1.4} km/s/Mpc, and Omega_b=0.0475+-0.0012 for LCDM, reducing the uncertainties of the WMAP9-only constraints by ~50%. When we do not assume flatness for LCDM, we obtain the curvature constraint Omega_k=-0.010_{-0.015}^{+0.013} from the DLS+WMAP9 combination, which however is not well constrained when WMAP9 is used alone. The dark energy equation of state parameter w is tightly constrained when Baryonic Acoustic Oscillation (BAO) data are added, yielding w=-1.02_{-0.09}^{+0.10} with the DLS+WMAP9+BAO joint probe. The addition of supernova constraints further tightens the parameter to w=-1.03+-0.03. Our joint constraints are fully consistent with the final Planck results and also the predictions of a LCDM universe.Comment: Accepted for publication in Ap

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

Abundances, masses, and weak-lensing mass profiles of galaxy clusters as a function of richness and luminosity in LambdaCDM cosmologies

We test the concordance LCDM cosmology by comparing predictions for the mean properties of galaxy clusters to observations. We use high-resolution N-body simulations of cosmic structure formation and semi-analytic models of galaxy formation to compute the abundance, mean density profile, and mass of galaxy clusters as a function of richness and luminosity, and we compare these predictions to observations of clusters in the Sloan Digital Sky Survey (SDSS) maxBCG catalogue. We discuss the scatter in the mass-richness relation, the reconstruction of the cluster mass function from the mass-richness relation, and fits to the weak-lensing cluster mass profiles. The impact of cosmological parameters on the predictions is investigated by comparing results from galaxy models based on the Millennium Simulation (MS) and another WMAP1 simulation to those from a WMAP3 simulation. We find that the simulated weak-lensing mass profiles and the observed profiles of the SDSS maxBCG clusters agree well in shape and amplitude. The mass-richness relations in the simulations are close to the observed relation, with differences lesssim 30%. The MS and WMAP1 simulations yield cluster abundances similar to those observed, whereas abundances in the WMAP3 simulation are 2-3 times lower. The differences in cluster abundance, mass, and density amplitude between the simulations and the observations can be attributed to differences in the underlying cosmological parameters, in particular the power spectrum normalisation sigma_8. Better agreement between predictions and observations should be reached with a normalisation $0.722<sigma_8<0.9$ (probably closer to the upper value), i.e. between the values underlying the two simulation sets.Comment: revised version taking reviewer's comments into account, submitted to MNRA

Contextual approach to quantum mechanics and the theory of the fundamental prespace

We constructed a Hilbert space representation of a contextual Kolmogorov model. This representation is based on two fundamental observables -- in the standard quantum model these are position and momentum observables. This representation has all distinguishing features of the quantum model. Thus in spite all ``No-Go'' theorems (e.g., von Neumann, Kochen and Specker,..., Bell) we found the realist basis for quantum mechanics. Our representation is not standard model with hidden variables. In particular, this is not a reduction of quantum model to the classical one. Moreover, we see that such a reduction is even in principle impossible. This impossibility is not a consequence of a mathematical theorem but it follows from the physical structure of the model. By our model quantum states are very rough images of domains in the space of fundamental parameters - PRESPACE. Those domains represent complexes of physical conditions. By our model both classical and quantum physics describe REDUCTION of PRESPACE-INFORMATION. Quantum mechanics is not complete. In particular, there are prespace contexts which can be represented only by a so called hyperbolic quantum model. We predict violations of the Heisenberg's uncertainty principle and existence of dispersion free states.Comment: Plenary talk at Conference "Quantum Theory: Reconsideration of Foundations-2", Vaxjo, 1-6 June, 200

Inter-species variation in colour perception

Inter-species variation in colour perception poses a serious problem for the view that colours are mind-independent properties. Given that colour perception varies so drastically across species, which species perceives colours as they really are? In this paper, I argue that all do. Specifically, I argue that members of different species perceive properties that are determinates of different, mutually compatible, determinables. This is an instance of a general selectionist strategy for dealing with cases of perceptual variation. According to selectionist views, objects simultaneously instantiate a plurality of colours, all of them genuinely mind-independent, and subjects select from amongst this plurality which colours they perceive. I contrast selectionist views with relationalist views that deny the mind-independence of colour, and consider some general objections to this strategy