We show that the so-called "post-Born" effects of weak lensing at 4th order are equivalent to lens-lens couplings in the Born Approximation. We demonstrate this by explicitly showing the equivalence of the canonical weak lensing approach at 4th order using the anisotropy remapping method, to that of the 4th order calculation of the lens-lens coupling effects using the Boltzmann equation approach that was first developed in [Phys. Rev. D89, 123006]. Furthermore, we argue that to incorporate true "post-Born" effects, i.e. taking into account non-straight photon paths, require the addition of a photon deflection term which has not been taken into account in the canonical formalism nor the Boltzmann method.
In this second paper, we develop an analytical theory of quasi-equatorial lensing by Kerr black holes. In this setting we solve perturbatively our general lens equation with displacement given in Paper I, going beyond weak-deflection Kerr lensing to third order in our expansion parameter epsilon, which is the ratio of the angular gravitational radius to the angular Einstein radius. We obtain new formulas and results for the bending angle, image positions, image magnifications, total unsigned magnification, and centroid, all to third order in epsilon and including the displacement. New results …
We present a new perspective on gravitational lensing. We describe a new extension of the weak lensing formalism capable of describing strongly lensed images. By integrating the non-linear geodesic deviation equation, the amplification matrix of weak lensing is generalised to a sum over independent amplification tensors of increasing rank. We show how an image distorted by a generic lens may be constructed as a sum over `roulettes', which are the natural curves associated with the independent spin modes of the amplification tensors. Highly distorted images can be constructed even for large sou…
The accuracy of mass estimates by gravitational lensing using the thin-lens approximation applied to Navarro-Frenk-White mass models with a soft truncation mechanism recently proposed by Baltz, Marshall and Oguri is studied. The gravitational lens scenario considered is the case of the inference of lens mass from the observation of Einstein rings (strong lensing). It is found that the mass error incurred by the simplifying assumption of thin lenses is below 0.5%. As a byproduct, the optimal tidal radius of the soft truncation mechanism is found to be at most 10 times the virial radius of the m…
To recognize gravitational wave lensing events and being able to differentiate between similar lens models will be of crucial importance once one will be observing several lensing events of gravitational waves per year. In this work, we study the lensing of gravitational waves in the context of LISA sources and wave-optics regime. While different papers before ours studied microlensing effects enhanced by simultaneous strong lensing, we focus on frequency (time) dependent phase effects produced by one lens that will be visible with only one lensed image. We will show how, in the interference r…
Current sky surveys have been conducted very accurately in order to understand our universe. One of the phenomena survey maps provide is gravitational effect. Albert Einstein (1936) first discussed the possibilities of gravitational lensing effects based on his theory of general relativity, which might give us some information about cosmology. We often categorize the effects by micro, weak, and strong lensing types. This paper focuses on the strong gravitational lensing, especially the double-source plane lens systems. It was recently recognized that the double lensing events can provide us wi…
We present the first detailed computations of wave optics effects in the gravitational lensing of binary systems. The field is conceptually rich, combining the caustic singularities produced in classical gravitational lensing with quantum (wave) interference effects. New techniques have enabled us to overcome previous barriers to computation. Recent developments in radio astronomy present observational opportunities which, while still futuristic, appear promising.
In this article, we present an overview of the new developments in problems of the plasma influence on the effects of gravitational lensing, complemented by pieces of new material and relevant discussions. Deflection of light in the presence of gravity and plasma is determined by a complex combination of various physical phenomena: gravity, dispersion, refraction. In particular, the gravitational deflection itself, in a homogeneous plasma without refraction, differs from the vacuum one and depends on the frequency of the photon. In an inhomogeneous plasma, chromatic refraction also takes place…
In this paper, we study lensing of 21cm intensity mapping (IM). Like in the cosmic microwave background (CMB), there is no first order lensing in intensity mapping. The first effects in the power spectrum are therefore of second and third order. Despite this, lensing of the CMB power spectrum is an important effect that needs to be taken into account, which motivates the study of the impact of lensing on the IM power spectrum. We derive a general formula up to third order in perturbation theory including all the terms with two derivatives of the gravitational potential, i.e. the dominant terms…
We study lensing by voids in Cubic Galileon and Nonlocal gravity cosmologies, which are examples of theories of gravity that modify the lensing potential. We find voids in the dark matter and halo density fields of N-body simulations and compute their lensing signal analytically from the void density profiles, which we show are well fit by a simple analytical formula. In the Cubic Galileon model, the modifications to gravity inside voids are not screened and they approximately double the size of the lensing effects compared to GR. The difference is largely determined by the direct effects of t…
The cross correlation between the thermal Sunyaev-Zeldovich (tSZ) effect and gravitational lensing in wide field has recently been measured. It can be used to probe the distribution of the diffuse gas in large scale structure, as well as inform us about the missing baryons. As for any lensing-based quantity, higher order lensing effects can potentially affect the signal. Here, we extend previous higher order lensing calculations to the case of tSZ-lensing cross correlations. We derive terms analogous to corrections due to the Born approximation, lens-lens coupling, and reduced shear up to four…
The weak lensing of cosmic web filaments is investigated in modified gravity (MOG) and it is demonstrated that the detected galaxies and baryonic gas of order $5-15 \%$ in filaments can with the enhanced value of the strength of gravity agree with the lensing data for filaments without dark matter.
We derive radial mass profiles of four strong lensing selected clusters which show prominent giant arcs (Abell 1703, SDSS J1446+3032, SDSS J1531+3414, and SDSS J2111-0115), by combining detailed strong lens modeling with weak lensing shear measured from deep Subaru Suprime-cam images. Weak lensing signals are detected at high significance for all four clusters, whose redshifts range from z=0.28 to 0.64. We demonstrate that adding strong lensing information with known arc redshifts significantly improves constraints on the mass density profile, compared to those obtained from weak lensing alone…
Weak gravitational lensing of background galaxies is a unique, direct probe of the distribution of matter in clusters of galaxies. We review several important aspects of cluster weak gravitational lensing together with recent advances in weak lensing techniques for measuring cluster lensing profiles and constraining cluster structure parameters.
Many weak lensing calculations make use of the Born approximation where the light ray is approximated by a straight path. We examine the effect of Born-corrections for lensing of the cosmic microwave background in an analytical approach by taking perturbative corrections to the geodesic into account. The resulting extra power in the lensing potential spectrum is comparable to the power generated by nonlinear structure formation and affects especially the polarisation spectra, leading to relative changes of the order of one per cent for the $E$-mode spectrum and up to 10 per cent on all scales …
We investigate correlations induced by gravitational lensing on simulated cosmic microwave background data of experiments with an incomplete sky coverage and their effect on inferences from the South Pole Telescope data. These correlations agree well with the theoretical expectations, given by the sum of super-sample and intra-sample lensing terms, with only a typically negligible $\sim$ 5% discrepancy in the amplitude of the super-sample lensing effect. Including these effects we find that lensing constraints are in $3.0σ$ or $2.1σ$ tension between the SPT polarization measurements and Planck…
The weak lensing effect on the cosmic microwave background (CMB) induces distortions in spatial pattern of CMB anisotropies, and statistical properties of CMB anisotropies become a weakly non-Gaussian field. We first summarize the weak lensing effect on the CMB (CMB lensing) in the presence of scalar, vector and tensor perturbations. Then we focus on the lensing effect on CMB statistics and methods to estimate deflection angles and their power spectrum. We end by summarizing recent observational progress and future prospect.
We investigate the impact of non-Gaussian lensing deflections on measurements of the CMB lensing power spectrum. We find that the false assumption of their Gaussianity significantly biases these measurements in current and future experiments at the percent level. The bias is detected by comparing CMB lensing reconstructions from simulated CMB data lensed with Gaussian deflection fields to reconstructions from simulations lensed with fully non-Gaussian deflection fields. The non-Gaussian deflections are produced by ray-tracing through snapshots of an N-body simulation and capture both the non-G…
Dark matter halos represent the highest density peaks in the matter distribution. Conversely, cosmic voids are under-dense patches of the universe. Probing the mass distribution of the universe requires various approaches, including weak gravitational lensing that subtly modifies the shape of distant sources, and Doppler lensing that changes the apparent size and magnitude of objects due to peculiar velocities. In this work, we adopt both gravitational and Doppler lensing effects to study the underlying matter distribution in and around cosmic voids/halos. We use the relativistic $N$-body code…
In this Letter, we report the observational constraints on the Hu-Sawicki $f(R)$ theory derived from weak lensing peak abundances, which are closely related to the mass function of massive halos. In comparison with studies using optical or x-ray clusters of galaxies, weak lensing peak analyses have the advantages of not relying on mass-baryonic observable calibrations. With observations from the Canada-France-Hawaii-Telescope Lensing Survey, our peak analyses give rise to a tight constraint on the model parameter $|f_{R0}|$ for $n=1$. The $95\%$ CL limit is $\log_{10}|f_{R0}| < -4.82$ given WM…
An incomplete sky coverage poses difficulties in the extraction of the weak lensing information from the CMB. We test the reconstruction of the weak lensing convergence from CMB maps to which masks of point sources have been applied. We use the quadratic estimator with a kernel with finite support acting in real space for a Planck simulation. We recover the lensing signal without significant loss of power or addition of spurious correlations, thus showing that masking defected pixels does not affect the reconstruction of the weak lensing convergence in real space.
Cosmic voids are an important probe of large-scale structure that can constrain cosmological parameters and test cosmological models. We present a new paradigm for void studies: void detection in weak lensing convergence maps. This approach identifies objects that relate directly to our theoretical understanding of voids as underdensities in the total matter field and presents several advantages compared to the customary method of finding voids in the galaxy distribution. We exemplify this approach by identifying voids using the weak lensing peaks as tracers of the large-scale structure. We fi…
Doppler lensing is the apparent change in object size and magnitude due to peculiar velocities. Objects falling into an overdensity appear larger on its near side, and smaller on its far side, than typical objects at the same redshifts. This effect dominates over the usual gravitational lensing magnification at low redshift. Doppler lensing is a promising new probe of cosmology, and we explore in detail how to utilize the effect with forthcoming surveys. We present cosmological simulations of the Doppler and gravitational lensing effects based on the Millennium simulation. We show that Doppler…
We study weak gravitational lensing by the cosmic large-scale structure of the 21-cm radiation background in the 3d-weak lensing formalism. The interplay between source distance measured at finite resolution, visibility and lensing terms is analysed in detail and the resulting total covariance $C_{\ell}(k,k')$ is derived. The effect of lensing correlates different multipoles through convolution, breaking the statistical homogeneity of the 21-cm radiation background. This homogeneity breaking can be exploited to reconstruct the lensing field $\hatϕ_{\ell m}(κ)$ and noise lensing reconstruction …
The weak gravitational lensing formalism can be extended to the strong lensing regime by integrating a nonlinear version of the geodesic deviation equation. The resulting "roulette" expansion generalises the notion of convergence, shear and flexion to arbitrary order. The independent coefficients of this expansion are screen space gradients of the optical tidal tensor which approximates to the usual lensing potential in the weak field limit. From lensed images, knowledge of the roulette coefficients can in principle be inverted to reconstruct the mass distribution of a lens. In this paper, we …
We discuss the gravitational lensing of gravitational wave signals from coalescing binaries. We delineate the regime where wave effects are significant from the regime where geometric limit can be used. Further, we focus on the effect of micro-lensing and the combined effect of strong lensing and micro-lensing. We find that micro-lensing combined with strong lensing can introduce time varying phase shift in the signal and hence can lead to detectable differences in the signal observed for different images produced by strong lensing. This, coupled with the coarse localization of signal source i…
Cosmic shear can only be measured where there are galaxies. This source-lens clustering (SLC) effect has two sources, intrinsic source clustering and cosmic magnification (magnification/size bias). Lensing tomography can suppress the former. However, this reduction is limited by the existence of photo-z error and nonzero redshift bin width. Furthermore, SLC induced by cosmic magnification cannot be reduced by lensing tomography. Through N-body simulations, we quantify the impact of SLC on the lensing power spectrum in the context of lensing tomography. We consider both the standard estimator a…
We demonstrate a method for reconstructing the weak lensing potential from the Lyman-$α$ forest data. We derive an optimal estimator for the lensing potential on the sky based on the correlation between pixels in real space. This method effectively deals with irregularly spaced data, holes in the survey, missing data and inhomogeneous noise. We demonstrate an implementation of the method with simulated spectra and weak lensing. It is shown that with a source density of $>\sim 0.5$ per square arcminutes and $\sim 200$ pixels in each spectrum ($λ/ Δλ= 1300$) the lensing potential can be reconstr…
The study of the Cosmic Microwave Background (CMB) lensing potential has established itself by now as a robust way of probing the physics of large-scale structure growth. The most common estimators of the lensing potential are derived under the assumption of Gaussianity of the matter distribution and in the Born approximation of the photon diffusion. In this paper we study the performance of quadratic estimators when applied to realistic sky maps extracted from multiple-lens ray tracing techniques in cosmological $N$-body simulations. These are expected to model accurately the effects due to t…
We present weak lensing mass estimates for a sample of 458 galaxy clusters from the redMaPPer Sloan Digital Sky Survey DR8 catalogue using Hyper Suprime-Cam weak lensing data. We develop a method to quickly estimate cluster masses from weak lensing shear and use this method to estimate weak lensing masses for each of the galaxy clusters in our sample. Subsequently, we constrain the mass-richness relation as well as the intrinsic scatter between the cluster richness and the measured weak lensing masses. When calculating the mass-richness relation for all clusters with a richness $λ>20$, we find…
Strong gravitational lensing is an important tool to probe the universe. In the theoretical analysis of gravitational lensing, it is assumed that continuous density profile can correctly describe the lens galaxy. But in fact this assumption has never been rigorously tested. In this paper, we discuss this issue, and point out that if we use discrete density profile to model the lens galaxy, then the position of the images does not change, but the magnification will be increased. Strongly lensed gravitational waves could test this conclusion in the future.
We investigate the accuracy of weak lensing simulations by comparing the results of five independently developed lensing simulation codes run on the same input $N$-body simulation. Our comparison focuses on the lensing convergence maps produced by the codes, and in particular on the corresponding PDFs, power spectra and peak counts. We find that the convergence power spectra of the lensing codes agree to $\lesssim 2\%$ out to scales $\ell \approx 4000$. For lensing peak counts, the agreement is better than $5\%$ for peaks with signal-to-noise $\lesssim 6$. We also discuss the systematic errors…
The cosmic microwave background (CMB) represents a unique source for the study of gravitational lensing. It is extended across the entire sky, partially polarized, located at the extreme distance of z=1100, and is thought to have the simple, underlying statistics of a Gaussian random field. Here we review the weak lensing of the CMB, highlighting the aspects which differentiate it from the weak lensing of other sources, such as galaxies. We discuss the statistics of the lensing deflection field which remaps the CMB, and the corresponding effect on the power spectra. We then focus on methods fo…
According to the theory of general relativity, masses deflect light in a way similar to convex glass lenses. This gravitational lensing effect is astigmatic, giving rise to image distortions. These distortions allow to quantify cosmic structures statistically on a broad range of scales, and to map the spatial distribution of dark and visible matter. We summarise the theory of weak gravitational lensing and review applications to galaxies, galaxy clusters and larger-scale structures in the Universe.
As the first paper in a series on the study of the galaxy-galaxy lensing from Sloan Digital Sky Survey Data Release 7 (SDSS DR7), we present our image processing pipeline that corrects the systematics primarily introduced by the Point Spread Function (PSF). Using this pipeline, we processed SDSS DR7 imaging data in $r$ band and generated a background galaxy catalog containing the shape information of each galaxy. Based on our own shape measurements of the galaxy images from SDSS DR7, we extract the galaxy-galaxy (GG) lensing signals around foreground spectroscopic galaxies binned in different …
The measurement of cosmic shear using weak gravitational lensing is a challenging task that involves a number of complicated procedures. We study in detail the systematic errors in the measurement of weak lensing Minkowski Functionals (MFs). Specifically, we focus on systematics associated with galaxy shape measurements, photometric redshift errors, and shear calibration correction. We first generate mock weak-lensing catalogs that directly incorporate the actual observational characteristics of the Canada-France-Hawaii Lensing Survey (CFHTLenS). We then perform a Fisher analysis using the lar…
To take full advantage of the unprecedented power of upcoming weak lensing surveys, understanding the noise, such as cosmic variance and geometry/mask effects, is as important as understanding the signal itself. Accurately quantifying the noise requires a large number of statistically independent mocks for a variety of cosmologies. This is impractical for weak lensing simulations, which are costly for simultaneous requirements of large box size (to cover a significant fraction of the past light cone) and high resolution (to robustly probe the small scale where most lensing signal resides). The…
The presence of mass inhomogeneities along the line of sight of propagation of light fromdistant objects can induce deflection in the flight path of the photon. This phenomenon is called as gravitational lensing. Lensing can have both distortion (shear) and isotropic magnification effects on the source. We studied the effect of lensing magnification on supernova (SN) Ia in this thesis. Presence of lensing would introduce a source of contamination to the brightness distribution of the source (SN Ia in our case). Thus it also enables one to compute the lensing effect indirectly from the Hubble d…
Cross-correlations between galaxy weak lensing (WL) and Cosmic Microwave Background (CMB) lensing are a powerful tool to probe matter fluctuations at intermediate redshifts and to detect residual systematics in either probe. In this paper, we study the cross-correlation of galaxy WL from the Hyper Suprime-Cam Subaru Strategic Program (HSC) first data release and CMB lensing from the final Planck data release, for HSC source galaxies at 0.3< z < 1.5. HSC is the deepest Stage-III galaxy WL survey, and provides both a great opportunity to study the high-redshift universe and new challenges relate…
We study the effects of gravitational lensing on the estimation of non-Gaussianity from the bispectrum of the cosmic microwave background (CMB) temperature anisotropies. We find that the effect of lensing on the bispectrum may qualitatively be described as a smoothing of the acoustic features analogous to the temperature power spectrum. In contrast to previous results, for a Planck-like experiment which is cosmic-variance limited to L=2000, we find that lensing causes no significant degradation of our ability to constrain the non-Gaussianity amplitude fNL for both local and equilateral configu…
We report a mass reconstruction of A1689 using Particle Based Lensing (PBL), a new technique for Strong+Weak lensing that allows a variable resolution depending on the data density and the signal-to-noise. Using PBL we also calculate the covariance matrix for the resulting mass map. The reconstruction of A1689 shows a secondary mass peak in the north-east direction confirming previous optical observations. This indicates that the central region of the cluster is still undergoing a weak merger. We have used this mass map to measure power ratios of the dark matter distribution and compared it to…
We infer gravitational lensing shear and convergence fields from galaxy ellipticity catalogs under a spatial process prior for the lensing potential. We demonstrate the performance of our algorithm with simulated Gaussian-distributed cosmological lensing shear maps and a reconstruction of the mass distribution of the merging galaxy cluster Abell 781 using galaxy ellipticities measured with the Deep Lens Survey. Given interim posterior samples of lensing shear or convergence fields on the sky, we describe an algorithm to infer cosmological parameters via lens field marginalization. In the most …
Gravitational and plasma lensing share the same mathematical formalism in the limit of geometrical optics. Both phenomena can be effectively described by a projected, two-dimensional deflection potential whose gradient causes an instantaneous light deflection in a single, thin lens plane. We highlight the differences in the time-delay and lensing equations that occur because plasma lensing is caused by a potential directly proportional to the deflecting electron number density and gravitational lensing is caused by a potential related to the deflecting mass density by a Poisson equation. Since…
We present results from the Wendelstein Weak Lensing (WWL) pathfinder project, in which we have observed three intermediate redshift Planck clusters of galaxies with the new 30'$\times 30$' wide field imager at the 2m Fraunhofer Telescope at Wendelstein Observatory. We investigate the presence of biases in our shear catalogues and estimate their impact on our weak lensing mass estimates. The overall calibration uncertainty depends on the cluster redshift and is below 8.1-15 per cent for $z \approx 0.27-0.77$. It will decrease with improvements on the background sample selection and the multipl…
We present a light-traces-mass (LTM) strong-lensing model of the massive lensing cluster MACS J2135.2-0102 ($z$=0.33; hereafter MACS2135), known in part for hosting the Cosmic Eye galaxy lens. MACS2135 is also known to multiply-lens a $z=$2.3 sub-mm galaxy near the Brightest Cluster Galaxy (BCG), as well as a prominent, triply-imaged system at a large radius of $\sim$37" south of the BCG. We use the latest available Hubble imaging to construct an accurate lensing model for this cluster, identifying six new multiply-imaged systems with the guidance of our LTM method, so that we have roughly qua…
Gravitationally lensed curved arcs provide a wealth of information about the underlying lensing distortions. Extracting precise lensing information from extended sources is a key component in many studies aiming to answer fundamental questions about the Universe. To maintain accuracy with increased precision, it is of vital importance to characterize and understand the impact of degeneracies inherent in lensing observables. In this work, we present a formalism to describe the gravitational lensing distortion effects resulting in curved extended arcs based on the eigenvectors and eigenvalues of…
Plasma lensing is the refraction of low-frequency electromagnetic rays due to cold free electrons in the universe. For sources at a cosmological distance, there is observational evidence of elongated, complex plasma structures along the line of sight requiring a multi-lens-plane description. To investigate the limits of single-plane plasma lensing, we set up a double-plane lens with a projected Gaussian electron density in each lens plane. We compare double-plane scenarios with corresponding effective single-plane configurations. Our results show how double-plane lenses can be distinguished fr…
Weak gravitational lensing leaves a characteristic imprint on the cosmic microwave background temperature and polarization angular power spectra. Here we investigate the possible constraints on the integrated lensing potential from future CMB angular spectra measurements expected from Planck and EPIC. We find that Planck and EPIC will constrain the amplitude of the integrated projected potential responsible for lensing at 6% and 1% level, respectively with very little sensitivity to the shape of the lensing potential. We discuss the implications of such a measurement in constraining dark energ…
For lensing galaxies we introduce a formal velocity dispersion sigma_lens, based on enclosed mass and the virial theorem. This is calculated from an ensemble of pixelated lens models, and found to be fairly model independent. A sample of 18 well-known early-type lensing galaxies and two clusters is found to be consistent with the equality of sigma_lens and the kinematic velocity dispersion sigma_obs. Both the early-type lensing galaxies and the clusters can thus be determined as being virialized. In a second step we calculate the I-band luminosity and the total mass content for the sample of l…
In this work we present a lensing study of Compact Groups (CGs) using data obtained from the high quality Canada-France-Hawaii Telescope Stripe 82 Survey. Using stacking techniques we obtain the average density contrast profile. We analyse the lensing signal dependence on the groups surface brightness and morphological content, for CGs in the redshift range $z = 0.2 - 0.4$. We obtain a larger lensing signal for CGs with higher surface brightness, probably due to their lower contamination by interlopers. Also, we find a strong dependence of the lensing signal on the group concentration paramete…
Numerical studies on the imaging and caustic properties of the singular isothermal sphere (SIS) under a wide range of external shear (from 0.0 to 2.0) are presented. Using a direct inverse-mapping formula for this lens system (Lee 2003), we investigate various lensing properties under both a low (i.e., γ < 1.0), and a high (i.e., γ > 1.0) shear case: image separations, total or individual magnifications, flux ratios of 2-images, maximum number of images, and lensing cross-sections. We systematically analyze the effective lensing cross-sections of double-lensing and quad-lensing systems based o…
