With increasingly large data sets, weak lensing measurements are able to measure cosmological parameters with ever greater precision. However this increased accuracy also places greater demands on the statistical tools used to extract the available information. To date, the majority of lensing analyses use the two point-statistics of the cosmic shear field. These can either be studied directly using the two-point correlation function, or in Fourier space, using the power spectrum. But analyzing weak lensing data inevitably involves the masking out of regions or example to remove bright stars from the field. Masking out the stars is common practice but the gaps in the data need proper handling. In this paper, we show how an inpainting technique allows us to properly fill in these gaps with only $N \log N$ operations, leading to a new image from which we can compute straight forwardly and with a very good accuracy both the pow er spectrum and the bispectrum. We propose then a new method to compute the bispectrum with a polar FFT algorithm, which has the main advantage of avoiding any interpolation in the Fourier domain. Finally we propose a new method for dark matter mass map reconstruction from shear observations which integrates this new inpainting concept. A range of examples based on 3D N-body simulations illustrates the results.
Constraints on an exact quintessence scalar-field model with an exponential potential are derived from gravitational lens statistics. An exponential potential can account for data from both optical quasar surveys and radio selected sources. Based on the Cosmic Lens All-Sky Survey (CLASS) sample, lensing statistics provides, for the pressureless matter density parameter, an estimate of Omega_{M0} = 0.31(-0.14)(+0.12).
We present ray tracing simulations combined with sets of large N-body simulations. Experiments were performed to explore, for the first time, statistical properties of fluctuations in angular separations of nearby light ray pairs (the so-called lensing excursion angle) induced by weak lensing by large-scale structures. We found that the probability distribution function (PDF) of the lensing excursion angles is not simply Gaussian but has an exponential tail. It is, however, found that the tail, or more generally non-Gaussian nature in the PDF has no significant impact on the weak lensing of th…
Gravitational lensing causes a correlation between a population of foreground large-scale structures and the observed number density of the background distant galaxies as a consequence of the flux magnification and the lensing area distortion. This correlation has not been taken into account in calculations of the theoretical predictions of the cosmic shear statistics but may cause a systematic error in a cosmic shear measurement. We examine its impact on the cosmic shear statistics using the semi-analytic approach. We find that the lensing magnification has no practical influence on the cosmi…
We present constraints on the cosmological constant lambda_0 and the density parameter Omega_0 from joint constraints from the analyses of gravitational lensing statistics of the Jodrell Bank-VLA Astrometric Survey (JVAS), optical gravitational lens surveys from the literature and CMB anisotropies. This is the first time that quantitative joint constraints involving lensing statistics and CMB anisotropies have been presented. Within the assumptions made, we achieve very tight constraints on both lambda_0 and Omega_0. These assumptions are cold dark matter models, no tensor components, no reion…
I present constraints on cosmological parameters in the lambda_0-Omega_0 plane from a joint analysis of gravitational lensing statistics (astro-ph/9904175) and the magnitude-redshift relation for Type Ia supernovae (astro-ph/9812133 and astro-ph/9805201). I discuss reasons why this particular combination of tests is important and how the constraints can be improved in the future. The lensing statistics and supernova results are not inconsistent, thus it is meaningful to determine joint constraints on lambda_0 and Omega_0 by combining the results from both tests. The quantity measured by the le…
We present a new approach to measure the mass function of dark matter halos and to discriminate models with differing values of Omega through weak gravitational lensing. We measure the distribution of peaks from simulated lensing surveys and show that the lensing signal due to dark matter halos can be detected for a wide range of peak heights. Even when the signal-to-noise is well below the limit for detection of individual halos, projected halo statistics can be constrained for halo masses spanning galactic to cluster halos. The use of peak statistics relies on an analytical model of the nois…
A complete catalogue of galaxy cluster models can be used to constrain cosmological parameters like $σ_8$, the amplitude of the initial density fluctuation spectrum. We focus here on two strong lensing statistics for clusters of galaxies: the fraction of rich Abell clusters that are critical to lensing, and the abundance of arcs in such clusters, especially the X-ray luminous ones. The specific aim of this paper is to constrain $σ_8$ for the standard Cold Dark Matter scenario within an Einstein-de Sitter universe.
By using the comoving distance, we derive an analytic expression for the optical depth of gravitational lensing, which depends on the redshift to the source and the cosmological model characterized by the cosmic mass density parameter $Ω_m$, the dark energy density parameter $Ω_x$ and its equation of state $ω_x = p_x/ρ_x$. It is shown that, the larger the dark energy density is and the more negative its pressure is, the higher the gravitational lensing probability is. This fact can provide an independent constraint for dark energy.
We consider an astrophysical system with a population of sources and a population of lenses. For each pair of source and lens, there is a thin on-axis tube-like volume behind the lens in which the radiation flux from the source is greatly increased due to gravitational lensing. Any objects (such as dust grains) which pass through such a thin tube will experience strong bursts of radiation, i.e., Extreme Gravitational Lensing Events (EGLE). We study the physics and statistics of EGLE for the case in which the shear is larger or comparable to the finite source size. We find that the presence of …
Future weak lensing surveys will directly probe the clustering of dark matter, in addition to providing a test for various cosmological models. Recent studies have provided us with the tools which can be used to construct the complete probability distribution function for convergence fields. It is also possible to construct the bias associated with the hot-spots in convergence maps. These techniques can be used in both the quasi-linear and the highly nonlinear regimes using various well developed numerical methods. We use these results here to study the weak lensing statistics of cosmological …
For a given source and lens pair, there is a thin on-axis tube-like volume behind the lens in which the radiation flux from the source is greatly increased due to gravitational lensing. Any objects (such as dust grains) which pass through such a thin tube will experience strong bursts of radiation, i.e., Extreme Gravitational Lensing Events (EGLE). We study the physics and statistics of EGLE for the case in which finite source size is more important than shear. One of the several possible significant astrophysical effects is investigated with an illustrative calculation.
We present a new non-parametric method for determining mean 3D density and mass profiles from weak lensing measurements around stacked samples of galaxies or clusters, that is, from measurement of the galaxy-shear or cluster-shear correlation functions. Since the correlation function is statistically isotropic, this method evades problems, such as projection of large-scale structure along the line of sight or halo asphericity, that complicate attempts to infer masses from weak lensing measurements of individual objects. We demonstrate the utility of this method in measuring halo profiles, gala…
We discuss the consistency of constraints in the lambda_0-Omega_0 plane from gravitational lensing statistics, the m-z relation for type Ia supernovae and CMB anisotropies, based on our own (published or unpublished) work and results from the literature.
We present a coherent theoretical framework for computing gravitational lensing effects and redshift-space distortions in an inhomogeneous universe and investigate their impacts on galaxy two-point statistics. Adopting the linearized FRW metric, we derive the gravitational lensing and the generalized Sachs-Wolfe effects that include the weak lensing distortion, magnification, and time delay effects, and the redshift-space distortion, Sachs-Wolfe, and integrated Sachs-Wolfe effects, respectively. Based on this framework, we first compute their effects on observed source fluctuations, separating…
We investigate statistical distributions of differences in gravitational-lensing deflections between two light rays, the so-called lensing excursion angles. A probability distribution function of the lensing excursion angles, which plays a key role in estimates of lensing effects on angular clustering of objects (such as galaxies, QSOs and also the CMB temperature map), is known to consist of two components; a Gaussian core and an exponential tail. We use numerical gravitational-lensing experiments in a Lambda-CDM cosmology for quantifying these two components. We especially focus on the physi…
Weak lensing surveys are expected to provide direct measurements of the statistics of the projected dark matter distribution. Most analytical studies of weak lensing statistics have been limited to quasilinear scales as they relied on perturbative calculations. On the other hand, observational surveys are likely to probe angular scales less than 10 arcminutes, for which the relevant physical length scales are in the nonlinear regime of gravitational clustering. We use the hierarchical ansatz to compute the multi-point statistics of the weak lensing convergence for these small smoothing angles.…
We present an analytical formulation of gravitational lensing using familiar triaxial power-law mass distributions, where the 3-dimensional mass density is given by $ρ(X,Y,Z) = ρ_0 [1 + (\frac{X}{a})^2 + (\frac{Y}{b})^2 + (\frac{Z}{c})^2]^{-ν/2}$. The deflection angle and magnification factor are obtained analytically as Fourier series. We give the exact expressions for the deflection angle and magnification factor. The formulae for the deflection angle and magnification factor given in this paper will be useful for numerical studies of observed lens systems. An application of our results to t…
Strong gravitational lensing is a useful probe of both the intrinsic properties of the lenses and the cosmological parameters of the universe. The large number of model parameters and small sample of observed lens systems, however, have made it difficult to obtain useful constraints on more than a few parameters from lensing statistics. Here we examine how the recent WMAP measurements help improve the constraining power of statistics from the radio lensing survey JVAS/CLASS. We find that the absence of theta>3'' lenses in CLASS places an upper bound of beta<1.25 (1.60) at 68% (95%) CL on the i…
Strong gravitational lensing by irregular mass distributions, such as galaxy clusters, is generally not well quantified by cross sections of analytic mass models. Computationally expensive ray-tracing methods have so far been necessary for accurate cross-section calculations. We describe a fast, semi-analytic method here which is based on surface integrals over high-magnification regions in the lens plane and demonstrate that it yields reliable cross sections even for complex, asymmetric mass distributions. The method is faster than ray-tracing simulations by factors of $\sim30$ and thus suita…
We investigate observational constraints from lensing statistics and high-z type Ia supernovae on flat cosmological models with nonrelativistic matter and an exotic fluid with equation of state, $p_x=(m/3 -1)ρ_x$. We show that agreement with both tests at the 68% confidence level is possible if the parameter $m$ is low ($m \lesssim 0.85$) and $0.24 \lesssim Ω_{m0} \lesssim 0.38$ with lower values of $Ω_{m0}$ corresponding to higher $m$. We find that a conventional cosmological constant model with $Ω_{m0}\simeq 0.33$ is the best fit model of the combined likelihood.
The self-accelerating braneworld model (DGP) seems to provide a simple alternative to the the standard $Λ$CDM cosmology to explain the current cosmic acceleration, which is strongly indicated by measurements of Type Ia supernovae, as well as other concordant observations. In this work, we investigate observational constraints on this scenario from gravitational lensing statistics using the Cosmic Lens All-Sky Survey (CLASS) lensing sample. We show that a large parameter space of the DGP model is in good agreement with this radio source gravitational lensing sample. In the flat case, $Ω_\mathrm…
The general idea of determining cosmological parameters with gravitational lensing statistics is outlined, and then recent work---with an emphasis on applicability to all cosmological models, observational bias, better statistics and robustness testing through numerical simulations---is discussed with relevance to a scheme originally introduced by Kochanek to avoid some of the uncertainties which plague other methods. The main result is that the observations at present---and probably in the future as well---are more indicative of intrinsic scatter than a hint of the correct cosmological model.
We describe an efficient algorithm for calculating the statistics of weak lensing by large-scale structure based on a tiled set of independent particle-mesh N-body simulations which telescope in resolution along the line of sight. This efficiency allows us to predict not only the mean properties of lensing observables such as the power spectrum, skewness and kurtosis of the convergence, but also their sampling errors for finite fields of view, which are themselves crucial for assessing the cosmological significance of observations. We find that the nongaussianity of the distribution substantia…
The deep imaging of the field of an observed lensing event by a cosmic string reveals many additional lensing events. We study the statistics of such string lensing. We derive explicit expressions for the distributions of image separations of lensing by a cosmic string and point out that they are quite sensitive to parameters which characterize the cosmic string, such as the redshift and tension of the cosmic string. Thus the statistics of string lensing events add new important information on the cosmic string which cannot be obtained from the detailed investigation of one lensing event.
We present new limits on cosmological parameters from the statistics of gravitational lensing, based on the recently revised knowledge of the luminosity function and internal dynamics of E/S0 galaxies that are essential in lensing high-redshift QSOs. We find that the lens models using updated Schechter parameters for such galaxies, derived from the recent redshift surveys combined with morphological classification, are found to give smaller lensing probabilities than earlier calculated. Inconsistent adoption of these parameters from a mixture of various galaxy surveys gives rise to systematic …
After a brief introduction to gravitational lensing theory, a rough overview of the types of gravitational lensing statistics that have been performed so far will be given. I shall then concentrate on recent results of galaxy-galaxy lensing, which indicate that galactic halos extend much further than can be probed via rotation of stars and gas.
Using the Eikonal approximation we study the effect of the smoothness parameter in the Dyer-Roeder equation. We calculate the optical depth for dark halos with NFW profile, for the abundance the Press-Schechter formalism is used. We focus our analysis on the cross section for multiple images (three). Different cosmologies are compared.
Arc statistics is known to be a powerful cosmological tool. Numerical lensing simulations show that orders of magnitude differences in the number of {\em giant} arcs on the whole sky are expected in different cosmological models. In this paper, we discuss the analytic and numerical methods in arc statistics and show that analytic models fail to reproduce the efficiency for strong lensing of more realistic numerical cluster models. Then, we discuss two recent extensions of the lensing simulations, i.e. the effects of cD galaxies in the lensing clusters and the impact of cluster mergers on arc s…
The topology of weak lensing fields is studied using the 2-dimensional genus statistic. Simulated fields of the weak lensing convergence are used to focus on the effect of nonlinear gravitional evolution and to model the statistical errors expected in observational surveys. For large smoothing angles, the topology is in agreement with the predictions from linear theory. On smoothing angles smaller than 10', the genus curve shows the non-Gaussian signatures of gravitational clustering and differs for open and flat cold dark matter models. Forthcoming surveys with areas larger than 10 square deg…
Fourier series solutions to the deflection and magnification by a family of three-dimensional cusped two power-law ellipsoidal mass distributions are presented. The cusped two power-law ellipsoidal mass distributions are characterized by inner and outer power-law radial indices and a break (or, transition) radius. The model family includes mass models mimicking Jaffe, Hernquist, and $η$ models and dark matter halo profiles from numerical simulations. The Fourier series solutions for the cusped two power-law mass distributions are relatively simple, and allow a very fast calculation even for a …
The principles of measuring the shapes of galaxies by a model-fitting approach are discussed in the context of shape-measurement for surveys of weak gravitational lensing. It is argued that such an approach should be optimal, allowing measurement with maximal signal-to-noise, coupled with estimation of measurement errors. The distinction between likelihood-based and Bayesian methods is discussed. Systematic biases in the Bayesian method may be evaluated as part of the fitting process, and overall such an approach should yield unbiased shear estimation without requiring external calibration fro…
We investigate the impact of the observed correlation between a galaxies shape and its surrounding density field on the measurement of third order weak lensing shear statistics. Using numerical simulations, we estimate the systematic error contribution to a measurement of the third order moment of the aperture mass statistic (GGG) from three-point intrinsic ellipticity correlations (III), and the three-point coupling between the weak lensing shear experienced by distant galaxies and the shape of foreground galaxies (GGI and GII). We find that third-order weak lensing statistics are typically m…
In the pre-WMAP, pre-Supernova-Ia-Hubble-diagram era, quasar lensing statistics stubbornly indicated low values of Omega_Lambda. In contrast, a number of recent lensing statistics studies either find the data support the standard Lambda-CDM picture, or simply take the standard cosmological parameters as a given. Have the data or the analyses changed or improved, and how? I review several of the ``historical'' and the more recent studies, and show that there is no particular measurement, assumption, or model parameter in the old studies that was grossly wrong. Instead, at least several effects,…
Weak lensing by large-scale mass inhomogeneities in the Universe induces correlations in the observed ellipticities of distant sources. We first review the harmonic analysis and statistics required of these correlations and discuss calculations for the predicted signal. We consider the ellipticity correlation function, the mean-square ellipticity, the ellipticity power spectrum, and a global maximum-likelihood analysis to isolate a weak-lensing signal from the data. Estimates for the sensitivity of a survey of a given area, surface density, and mean intrinsic source ellipticity are presented. …
We investigate the effect of weak gravitational lensing in the limit of small angular scales where projected galaxy clustering is strongly nonlinear. This is the regime likely to be probed by future weak lensing surveys. We use well-motivated hierarchical scaling arguments and the plane-parallel approximation to study multi-point statistical properties of the convergence field. These statistics can be used to compute the vertex amplitudes in tree models of hierarchical clustering; these can be compared with similar measurements from galaxy surveys, leading to a powerful probe of galaxy bias.
Weak gravitational lensing surveys have the potential to directly probe mass density fluctuation in the universe. Recent studies have shown that it is possible to model the statistics of the convergence field at small angular scales by modeling the statistics of the underlying density field in the highly nonlinear regime. We propose a new method to model the complete probability distribution function of the convergence field as a function of smoothing angle and source redshift. The model relies on a hierarchical ansatz for the behavior of higher order correlations of the density field. We comp…
The probability distribution of lens image separations is calculated for the ``standard'' gravitational lensing statistics model in an arbitrary, flat Robertson-Walker universe, where lensing galaxies are singular isothermal spheres that follow the Schechter luminosity function. In a flat universe, the probability distribution is independent of the source distribution in space and in brightness. The distribution is compared with observed multiple-image lens cases through Monte-Carlo simulations and the Kolmogorov-Smirnov test. The predicted distribution depends on the shape of the angular sele…
I investigate the effects of source clustering on the weak lensing statistics, more particularly on the statistical properties of the local convergence, kappa, at large angular scales. The Perturbation Theory approach shows that the variance is not affected by source clustering at leading order but higher order moments such as the third and fourth moments can be. I compute the magnitude of these effects in case of an Einstein-de Sitter Universe for the angular top-hat filtered convergence. In these calculations the so-called Broadhurst and multiple lens coupling effects are neglected. The sour…
We present a fast, arbitrarily accurate method to simulate the effect of gravitational lensing of the Cosmic Microwave Background anisotropies and polarization fields by large scale structures. We demonstrate the efficiency and accuracy of the method and exhibit their dependence on the algorithm parameters.
Standard cosmology has many successes on large scales, but faces some fundamental difficulties on small, galactic scales. One such difficulty is the cusp/core problem. High resolution observations of the rotation curves for dark matter dominated low surface brightness (LSB) galaxies imply that galactic dark matter halos have a density profile with a flat central core, whereas N-body structure formation simulations predict a divergent (cuspy) density profile at the center. It has been proposed that this problem can be resolved by stellar feedback driving turbulent gas motion that erases the ini…
The weak lensing surveys have the potential to probe directly the clustering statistics of dark matter in the universe. Recent studies have shown that it is possible to predict analytically the whole probability distribution function (pdf) and the bias associated with the collapsed objects in the highly non-linear regime using the hierarchical ansatz. We extend such studies to the quasi-linear regime where the hierarchical ansatz is replaced by the tree-level perturbative calculations to an arbitrary order. It is shown how the generating function techniques can be coupled with the perturbative…
A small volume of space, nearly on-axis behind a gravitational lens with respect to a given source, will receive a greatly increased radiation flux. In the idealized case of a point mass lens acting on a point source in complete isolation, the volume will approach zero only as the flux tends to infinity; in fact, the volume weighted rms flux is divergent. In realistic cases, finite source size and the effects of other gravitational deflections (i.e., non-zero shear) limit the maximum flux and considerably complicate the physics, but very large fluxes are still produced in small volumes. We con…
This paper aims to study the use of future SNAP data together with the result of searches for strong gravitational lenses in future large quasar surveys to constrain the Generalized Chaplygin Gas (GCG) model. The GCG is considered as a possible unification scheme for dark matter-dark energy. It is found that both experiments should be able to place important constraints on the model, especially when both tests are used together.
We present constraints on the cosmological constant $λ_{0}$ from gravitational lensing statistics of the Jodrell Bank-VLA Astrometric Survey (JVAS). Although this is the largest gravitational lens survey which has been analysed, cosmological constraints are only comparable to those from optical surveys. This is due to the fact that the median source redshifts of JVAS are lower, which leads to both relatively fewer lenses in the survey and a weaker dependence on the cosmological parameters. Although more approximations have to be made than is the case for optical surveys, the consistency of the…
Possibly the only unambiguous verification that gamma-ray bursts (GRBs) are at cosmological distances would be the observation of multiple images of a gravitationally lensed burst. Each images would arrive at a different time, but exhibit identical light curves. We improve upon previous calculations of GRB lensing by using revised cosmological burst models based upon better knowledge of burst spectra, and we consider several sets of cosmological parameters. Only lensing by the known population of galaxies is considered, and we compute the lensing rate and amplification bias using three differe…
We investigate the potential of weak gravitational lensing maps to differentiate between distinct cosmological models, considering cosmic variance due to a limited map extension and the presence of noise. We introduce a measure of the differentiation between two models under a chosen lensing statistics. That enables one to determine in which circumstances (map size and noise level), and for which lensing measures two models can be differentiated at a desired confidence level. As an application, we simulate convergence maps for three cosmological models (SCDM, OCDM, and $Λ$CDM), calculate sever…
Inflationary cosmologies predict Gaussian primordial fluctuations, but subsequent gravitational lensing of the CMB disturbs its Gaussianity. Knowledge of the specific signature of lensing is necessary to distinguish a lensed Gaussian sky from an intrinsically non-Gaussian one. In this paper we investigate the pattern of non-Gaussian features in the CMB resulting from gravitational lensing, both analytically and numerically. We describe the lensed CMB temperature distribution using the formalism of generating functionals and obtain the complete picture of emerging non-Gaussian effects. To test …
Strong gravitational lensing has traditionally been one of the few phenomena said to oppose a large cosmological constant; many analyses of lens statistics have given upper limits on $Ω_Λ$ that are marginally inconsistent with the concordance cosmology. Those conclusions were based on models where the predicted number counts of galaxies at moderate redshifts (z~0.5-1) increased significantly with $Ω_Λ$. I argue that the models should now be calibrated by counts of distant galaxies. When this is done lens statistics lose most of their sensitivity to the cosmological constant.
Many recent studies have demonstrated that scaling arguments, such as the so-called hierarchical {\em ansatz}, are extremely useful in understanding the statistical properties of weak gravitational lensing. This is especially true on small angular scales (i.e. at high resolution), where the usual perturbative calculations of matter clustering no longer apply. We build on these studies in order to develop a complete picture of weak lensing at small smoothing angles. In particular, we study the full probability distribution function, bias and other multipoint statistics for the ``hot spots'' of …
We examine the usefulness of the strong lensing statistics to constrain the evolution of the number density of lensing galaxies by adopting the values of the cosmological parameters determined by recent WMAP observation. For this purpose, we employ the lens-redshift test proposed by Kochanek (1992) and constrain the parameters in two evolution models, simple power-law model characterized by the power law indexes $nu_{n}$ and $ν_{v}$ and the evolution model by Mitchell et al. (2005) based on CDM structure formation scenario. We use the well-defined lens sample from the Sloan Digital Sky Survey …
Semi-analytical models of galaxy formation can be used to predict the evolution of the number density of early-type galaxies as a function of the circular velocity at the virial radius, v_{c,vir}. Gravitational lensing probability and separation distribution on the other hand are sensitive to the velocity dispersion (or circular velocity) at about the effective radius. We adopt the singular isothermal ellipsoid (SIE) lens model to estimate the velocity dispersion at the effective radius. We use radio lenses from the Cosmic Lens All-Sky Survey and the PMN-NVSS Extragalactic Lens Survey to study…
The distortion of the images of faint high-redshift galaxies can be used to probe the intervening mass distribution. This weak gravitational lensing effect has been used recently to study the (projected) mass distribution of several clusters at intermediate and high redshifts. In addition, the weak lensing effect can be employed to detect (dark) matter concentrations in the Universe, based on their mass properties alone. Thus it is feasible to obtain a mass-selected sample of `clusters', and thereby probe the full range of their mass-to-light ratios. We study the expected number density of suc…
Density fluctuations in the matter distribution lead to distortions of the images of distant galaxies through weak gravitational lensing effects. This provides an efficient probe of the cosmological parameters and of the density field. In this article, we investigate the statistical properties of the convergence due to weak gravitational lensing by non-linear structures (i.e. we consider small angular windows $θ\la 1'$). Previous studies have shown how to relate the second and third order moments of the convergence to those of the density contrast while models based on the Press-Schechter pres…
Weak gravitational lensing is considered to be one of the most powerful tools to study the mass and the mass distribution of galaxy clusters. However, weak lensing mass reconstructions are plagued by the so-called mass-sheet degeneracy--the surface mass density κof the cluster can be determined only up to a degeneracy transformation κ\to κ' = λκ+ (1 -λ), where λis an arbitrary constant. This transformation fundamentally limits the accuracy of cluster mass determinations if no further assumptions are made. We describe here a method to break the mass-sheet degeneracy in weak lensing mass maps us…
Weak gravitational lensing is responsible for the shearing and magnification of the images of high-redshift sources due to the presence of intervening matter. The distortions are due to fluctuations in the gravitational potential, and are directly related to the distribution of matter and to the geometry and dynamics of the Universe. As a consequence, weak gravitational lensing offers unique possibilities for probing the Dark Matter and Dark Energy in the Universe. In this review, we summarise the theoretical and observational state of the subject, focussing on the statistical aspects of weak …
We investigate the weak gravitational lensing effect due to the large-scale structure of the universe on two-point correlations of local maxima ({\em hotspots}) in the 2D sky map of the cosmic microwave background (CMB) anisotropy. According to the Gaussian random statistics as most inflationary scenarios predict, the hotspots are discretely distributed with some {\em characteristic} angular separations on the last scattering surface owing to oscillations of the CMB angular power spectrum. The weak lensing then causes pairs of hotspots which are separated with the characteristic scale to be ob…
We reanalyse optical gravitational lens surveys from the literature in order to determine relative probabilities in the $λ_{0}$-$Ω_{0}$ plane, using a softened singular isothermal sphere lens model. In addition, we examine a portion of the $λ_{0}$-$Ω_{0}$ plane which includes all viable cosmological models; this is vital for comparison with other cosmological tests. The results are, within the errors, consistent with those of more specialised analyses, such as those concerning upper limits on $λ_{0}$ in a flat universe. We note that gravitational lensing statistics can provide a quite robust L…
{}From the lensing properties of a numerically simulated cluster, from the statistical properties of the giant arcs produced by the cluster, and from comparing the cluster properties derived both from lensing and from the X-ray properties of the intracluster gas, we conclude (1) that clusters may be significantly more efficient for lensing than estimated from their velocity dispersion on the basis of iso- thermal-sphere models, (2) that the discrepancy between cluster core radii derived from lensing and from their X-ray surface brightness may be understood assuming that the intracluster gas wa…
We study the deflection of light in the background of a "wiggly" cosmic string, and investigate whether it is possible to detect cosmic strings by means of weak gravitational lensing. For straight strings without small-scale structure there are no signals. In the case of strings with small-scale structure leading to a local gravitational attractive force towards the string, there is a small signal, namely a preferential elliptical distortion of the shape of background galaxies in the direction corresponding to the projection of the string onto the sky. The signal can be statistically distingui…
Measuring the distribution of mass on galaxy cluster scales is a crucial test of the Lambda CDM model, providing constraints on the nature of dark matter. Recent work investigating mass distributions of individual galaxy clusters using gravitational lensing has illuminated potential inconsistencies between the predictions of structure formation models relating halo mass to concentration and those relationships as measured in massive clusters. However, such analyses typically employ only simple spherical halo models with canonical NFW slopes, while the halos formed in simulations show a range o…
