The frequency and effects of multiple weak deflections in galaxy-galaxy lensing are investigated via Monte Carlo simulations. The lenses in the simulations are galaxies with known redshifts and known rest-frame blue luminosities. The frequency of multiple deflections above a given threshold shear value is quantified for discrete source redshifts, as well as for a set of sources that are broadly distributed in redshift space. In general, the closest lens in projection on the sky is not the only lens for a given source. In addition, ~50% of the time the closest lens is not the most important lens for a given source. Compared to a naive single-deflection calculation in which only the lensing due to the closest weak lens is considered, a full multiple-deflection calculation yields a higher net shear for individual sources, as well as a higher mean tangential shear around the lens centers. The full multiple-deflection calculation also shows that galaxy-galaxy lensing may contribute a substantial amount to cosmic shear on small angular scales. The degree to which galaxy-galaxy lensing contributes to the small-scale cosmic shear is, however, quite sensitive to the mass adopted for the halos of L_B* galaxies. Changing the halo mass by a factor of ~2.5 changes the contribution of galaxy-galaxy lensing to the cosmic shear by a factor of ~3 on scales of order 1 arcmin. The contribution of galaxy-galaxy lensing to cosmic shear decreases rapidly with angular scale and extrapolates to zero at scales of order 5 arcmin. This last result is roughly independent of the halo mass and suggests that for scales greater than about 5 arcmin, cosmic shear is insensitive to the details of the gravitational potentials of large galaxies.
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…
Weak gravitational lensing alters the apparent separations between observed sources, potentially affecting clustering statistics. We derive a general expression for the lensing deflection which is valid for any three-point statistic, and investigate its effect on the three-point clustering correlation function. We find that deflection of the clustering correlation function is greatest at around $z=2$. It is most prominent in regions where the correlation function varies rapidly, in particular at the baryon acoustic oscillation scale where it smooths out the peaks and troughs, reducing the peak…
The smaller the angular scales on which the anisotropies of the cosmic microwave background (CMB) are probed the more important their distortion due to gravitational lensing becomes. Here we investigate the maxima and minima of the CMB lensing deflection field using general extreme value statistics. Since general extreme value statistics applies to uncorrelated data in first place we consider appropriately low-pass filtered deflection maps. Besides the suppression of correlations filtering is required for another reason: The lensing field itself is not directly observable but needs to be (stat…
A standard method to study the mass distribution in galaxy clusters is through strong lensing of background galaxies in which the positions of multiple images of the same source constrain the surface mass distribution of the cluster. However, current parametrized mass models can often only reproduce the observed positions to within one or a few arcsec which is worse than the positional measurement uncertainty. One suggested explanation for this discrepancy is the additional perturbations of the path of the light ray caused by matter density fluctuations along the line of sight. We investigate …
It is usually assumed that the ellipticity power spectrum measured in weak lensing observations can be expressed as an integral over the underlying matter power spectrum. This is true at second order in the gravitational potential. We extend the standard calculation, constructing all corrections to fourth order in the gravitational potential. There are four types of corrections: corrections to the lensing shear due to multiple-deflections; corrections due to the fact that shape distortions probe the reduced shear $γ/(1-κ)$ rather than the shear itself; corrections associated with the non-linea…
When a cosmic microwave background (CMB) photon travels from the surface of last scatter through spacetime metric perturbations, the polarization vector may rotate about its direction of propagation. This gravitational rotation is distinct from, and occurs in addition to, the lensing deflection of the photon trajectory. This rotation can be sourced by linear vector or tensor metric perturbations and is fully coherent with the curl deflection field. Therefore, lensing corrections to the CMB polarization power spectra as well as the temperature-polarization cross-correlations due to non-scalar p…
Stable massive neutral particles emitted by astrophysical sources undergo deflection under the gravitational potential of our own galaxy. The deflection angle depends on the particle velocity and therefore non-relativistic particles will be deflected more than relativistic ones. If these particles can be detected through neutrino telescopes, cosmic ray detectors or directional dark matter detectors, their arrival directions would appear aligned on the sky along the source-lens direction. On top of this deflection, the arrival direction of non-relativistic particles is displaced with respect to…
The influence of plasma on different effects of gravitational lensing is reviewed. Using the Hamiltonian approach for geometrical optics in a medium in the presence of gravity, an exact formula for the photon deflection angle by a black hole (or another body with a Schwarzschild metric) embedded in plasma with a spherically symmetric density distribution is derived. The deflection angle in this case is determined by the mutual combination of different factors: gravity, dispersion, and refraction. While the effects of deflection by the gravity in vacuum and the refractive deflection in a nonhom…
We produce lensing potential and deflection-angle maps in order to simulate CMB weak-lensing via ray-tracing through the COupled Dark Energy Cosmological Simulations (CoDECS). The constructed maps reflect the N-body cosmic structures on a range of scales going from the arcminute to the degree scale. We investigate the variation of the lensing pattern due to the DE dynamics, characterised by different background and perturbation behaviours as a consequence of the interaction between the DE field and CDM. We study the results from three models differing in the background and perturbations evolut…
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…
We present the optimal convergence and shear estimators for lensing reconstruction from the cosmic microwave background temperature field. This generalizes the deflection estimator, is sensitive to non-lensing modes, provides internal consistency checks, and is always at least as optimal. Previously, these estimators were only known in the squeezed limit. This paper decomposes convergence and shear fields into cosine and sine waves and the lensed correlation function is then Taylor expanded in the wave amplitudes. Maximizing the likelihood function gives the optimal estimators for the converge…
We calculate the deflection angle, as well as the positions and magnifications of the lensed images, in the case of covariant $f(T)$ gravity. We first extract the spherically symmetric solutions for both the pure-tetrad and the covariant formulation of the theory, since considering spherical solutions the extension to the latter is crucial, in order for the results not to suffer from frame-dependent artifacts. Applying the weak-field, perturbative approximation we extract the deviations of the solutions comparing to General Relativity. Furthermore, we calculate the deflection angle and then th…
Weak gravitational lensing changes the angular power spectra of the cosmic microwave background (CMB) temperature and polarization in a characteristic way containing valuable information for cosmological parameter estimation and weak lensing reconstructions. So far, analytical expressions for the lensed CMB power spectra assume the probability density function (PDF) of the lensing excursion angle to be Gaussian. However, coherent light deflection by nonlinear structures at low redshifts causes deviations from a pure Gaussian PDF. Working in the flat-sky limit we develop a method for computing …
Lensing of the CMB is an important effect, and is usually modelled by remapping the unlensed CMB fields by a lensing deflection. However the lensing deflections also change the photon path so that the emission angle is no longer orthogonal to the background last-scattering surface. We give the first calculation of the emission-angle corrections to the standard lensing approximation from dipole (Doppler) sources for temperature and quadrupole sources for temperature and polarization. We show that while the corrections are negligible for the temperature and E-mode polarization, additional large-…
We compute the deflection angle to order (m/r_0)^2 and m/r_0*Lambda r_0^2 for a light ray traveling in a flat LambdaCDM cosmology which encounters a completely condensed mass region. We use a Swiss cheese model for the inhomogeneities and find that the most significant correction to the Einstein angle occurs not because of the non-linear terms but instead occurs because the condensed mass is embedded in a background cosmology.The Swiss cheese model predicts a decrease in the deflection angle of ~2% for weakly lensed galaxies behind the rich cluster A1689, and that the reduction can be as large…
We explore a new realisation of the galactic scale dynamics via gravitational lensing phenomenon in power-law $f(R)$ gravity theory of the type $f(R)\propto R^{1+δ}$ with $δ<<1$ for interpreting the clustered dark matter effects. We utilize the single effective point like potential (Newtonian potential + $f(R)$ background potential) obtained under the weak field limit to study the combined observations of galaxy rotation curve beyond the optical disk size and their lensing profile in $f(R)$ frame work. We calculate the magnitude of light deflection angle with the characteristic length scale (b…
We investigate the weak lensing corrections to the cosmic microwave background temperature anisotropies considering effects beyond the Born approximation. To this aim, we use the small deflection angle approximation, to connect the lensed and unlensed power spectra, via expressions for the deflection angles up to third order in the gravitational potential. While the small deflection angle approximation has the drawback to be reliable only for multipoles $\ell\lesssim 2500$, it allows us to consistently take into account the non-Gaussian nature of cosmological perturbation theory beyond the lin…
Debate persists as to whether the cosmological constant $Λ$ can directly modify the power of a gravitational lens. With the aim of reestablishing a consensus on this issue, I conduct a comprehensive analysis of gravitational lensing in the Schwarzschild--de Sitter spacetime, wherein the effects of $Λ$ should be most apparent. The effective lensing law is found to be in precise agreement with the $Λ=0$ result: $α_\mathrm{eff} = 4m/b_\mathrm{eff}+15πm^2/4b_\mathrm{eff}^2 +O(m^3/b_\mathrm{eff}^3)$, where the effective bending angle $α_\mathrm{eff}$ and impact parameter $b_\mathrm{eff}$ are define…
We study non-perturbatively the effect of the deflection angle on the BAO wiggles of the matter power spectrum in real space. We show that from redshift z~2 this introduces a dispersion of roughly 1 Mpc at BAO scale, which corresponds approximately to a 1% effect. The lensing effect induced by the deflection angle, which is completely geometrical and survey independent, smears out the BAO wiggles. The effect on the power spectrum amplitude at BAO scale is about 0.1% for z~2 and 0.2% for z~4. We compare the smoothing effects induced by the lensing potential and non-linear structure formation, s…
We present a novel test of general relativity (GR): measuring the geometric component of the time delay due to gravitational lensing. GR predicts that photons and gravitational waves follow the same geodesic paths and thus experience the same geometric time delay. We show that for typical systems, the time delays are tens of seconds, and thus can dominate over astrophysical delays in the timing of photon emission. For the case of GW 170817, we use a multi-plane lensing code to evaluate the time delay due to four massive halos along the line of sight. From literature mass and distance measureme…
We estimate the changes in solar system tests of general relativity when "dark energy" arises from a Weyl scaling invariant action, using the modified Schwarzschild-like spherically symmetric solution obtained in this case by Adler and Ramazano\vglu. We show that the standard results of general relativity are modified by amounts that are far below current experimental errors. However, because the metric is not conformally flat when the central mass $M$ vanishes, there is a contribution to light deflection proportional to the cosmological constant $Λ$, with opposite sign to the one proportional…
A hundred years ago, two British expeditions measured the deflection of starlight by the sun's gravitational field, confirming the prediction made by Einstein's General theory of Relativity. One hundred years later many physicists around the world are involved in studying the consequences and use as a research tool, of the deflection of light by gravitational fields, a discipline that today receives the generic name of Gravitational Lensing. The present review aims to commemorate the centenary of Einstein's Eclipse expeditions by presenting a historical perspective of the development and miles…
We systematically derive full-sky formulae for the weak lensing power spectra generated by scalar, vector and tensor perturbations from the total angular momentum (TAM) method. Based on both the geodesic and geodesic deviation equations, we first give the gauge-invariant expressions for the deflection angle and Jacobi map as observables of the CMB lensing and cosmic shear experiments. We then apply the TAM method, originally developed in the theoretical studies of CMB, to a systematic derivation of the angular power spectra. The TAM representation, which characterizes the total angular depende…
The higher dimensional Weyl curvature induces on the brane a new source of gravity. This Weyl fluid of geometrical origin (reducing in the spherically symmetric, static configuration to a dark radiation and dark pressure) modifies space-time geometry around galaxies and has been shown to explain the flatness of galactic rotation curves. Independent observations for discerning between the Weyl fluid and other dark matter models are necessary. Gravitational lensing could provide such a test. Therefore we study null geodesics and weak gravitational lensing in the dark radiation dominated region o…
In this paper we examine cosmological weak lensing on non-linear scales and show that there are Newtonian and relativistic contributions and that the latter can also be extracted from standard Newtonian simulations. We use the post-Friedmann formalism, a post-Newtonian type framework for cosmology, to derive the full weak-lensing deflection angle valid on non-linear scales for any metric theory of gravity. We show that the only contributing term that is quadratic in the first order deflection is the expected Born correction and lens-lens coupling term. We use this deflection angle to analyse t…
We study the observational signature of vector metric perturbations through the effect of weak gravitational lensing. In the presence of vector perturbations, the non-vanishing signals for B-mode cosmic shear and curl-mode deflection angle, which have never appeared in the case of scalar metric perturbations, naturally arise. Solving the geodesic and geodesic deviation equations, we drive the full-sky formulas for angular power spectra of weak lensing signals, and give the explicit expressions for E-/B-mode cosmic shear and gradient-/curl-mode deflection angle. As a possible source for seeding…
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…
