WEAK GRAVITATIONAL LENSING - Review and applications of weak gravitational lensing

Oct 4, 2026

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We review theory and applications of weak gravitational lensing, beginning with Friedmann-Lemaître cosmological models and then developing the gravitational lensing formalism and light propagation in arbitrary space-times. The work explains how weak-lensing signatures can be measured and demonstrates applications ranging from galaxy-cluster mass reconstruction and large-scale structure lensing to QSO-galaxy correlations. It also covers lensing by galaxies and weak lensing of the cosmic microwave background.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages85

Reading Time3 h 34 min

AccessFree to download

Abstract

1. Introduction

1.1. Gravitational Light Deﬂection

2. Weak-lensing measurement and applications

WEAK GRAVITATIONAL LENSING MATTHIAS BARTELMANN1 AND PETER SCHNEIDER1;2 1 MAX-PLANCK-INSTITUT FR ASTROPHYSIK, P. O. BOX 1523, D–85740 GARCHING, GERMANY 2 INSTITUT FR ASTROPHYSIK UND EXTRATERRESTRISCHE FORSCHUNG, UNIVERSITT BONN AUF DEM HGEL 71, D–53121 BONN, GERMANY to appear in Physics Reports ABSTRACT We review theory and applications of weak gravitational lensing. After summarising Friedmann-Lematre cosmological models, we present the formalism of gravitational lensing and light propagation in arbitrary space-times. We discuss how weak-lensing effects can be measured. The formalism is then applied to reconstructions of galaxycluster mass distributions, gravitational lensing by large-scale matter distributions, QSO-galaxy correlations induced by weak lensing, lensing of galaxies by galaxies, and weak lensing of the cosmic microwave background. 1 . INTRODUCTION 1.1. Gravitational Light Deﬂection Light rays are deﬂected when they propagate through an inhomogeneous gravitational ﬁeld. Although several researchers had speculated about such an effect well before the advent of General Relativity (see Schneider et al. 1992 for a historical account), it was Einstein’s theory which elevated the deﬂection of light by masses from a hypothesis to a ﬁrm prediction. Assuming light behaves like a stream of particles, its deﬂection can be calculated within Newton’s theory of gravitation, but General Relativity predicts that the effect is twice as large. A light ray grazing the surface of the Sun is deﬂected by 1 : 75 arc seconds compared to the 0 : 87 arc seconds predicted by Newton’s theory. The conﬁrmation of the larger value in 1919 was perhaps the most important step towards accepting General Relativity as the correct theory of gravity (Eddington 1920) . Cosmic bodies more distant, more massive, or more compact than the Sun can bend light rays from a single source sufﬁciently strongly so that multiple light rays can reach the observer. The observer sees an image in the direction of each ray arriving at their position, so that the source appears multiply imaged. In the language of General Relativity, there may exist more than one null geodesic connecting the world-line of a source with the observation event. Although predicted long before, the ﬁrst multiple-image system was discovered only in 1979 (Walsh et al. 1979) . From then on, the ﬁeld of gravitational lensing developed into one of the most active subjects of astrophysical research. Several dozens of multiply-imaged sources have since been found. Their quantitative analysis provides accurate masses of, and in some cases detailed information on, the deﬂectors. An example is shown in Fig. 1. Tidal gravitational ﬁelds lead to differential deﬂection oflight bundles. The size and shape of their cross sections are therefore changed. Since photons are neither emitted nor absorbed in the process of gravitational light deﬂection, the surface brightness of lensed sources remains unchanged. Changing the size of the cross section of a light bundle therefore changes the ﬂux observed from a source. The different images in multiple-image systems generally have different ﬂuxes. The images of extended sources, i.e. sources which can observationally be resolved, are deformed by the gravitational tidal ﬁeld. Since astronomical sources like galaxies are not intrinsically circular, this deformation is generally very difﬁcult to identify in individual images. In some cases, however, the distortion is strong enough to be read- FIG . 1.—The gravitational lens system 2237+0305 consists ofa nearby spiral galaxy at redshift zd = 0 : 039 and four images of a background quasar with redshift zs = 1 : 69. It was discovered by Huchra et al.(1985) . The image was taken by the Hubble Space Telescope and shows only the innermost region of the lensing galaxy. The central compact source is the bright galaxy core, the other four compact sources are the quasar images. They differ in brightness bec

FAQs

What does weak gravitational lensing study in this work?

It reviews theory and applications of weak gravitational lensing, including how light propagates through inhomogeneous gravitational fields and how weak-lensing effects are measured.

How is gravitational light deflection explained and contrasted with Newtonian gravity?

Light rays are deflected by inhomogeneous gravitational fields; the paper notes that General Relativity predicts the effect is twice as large as the Newtonian calculation for a grazing ray near the Sun.

What are examples of applications discussed for weak lensing?

The text applies the formalism to reconstruct galaxy-cluster mass distributions, study lensing by large-scale matter, analyze QSO-galaxy correlations, examine galaxy-on-galaxy lensing, and address weak lensing of the cosmic microwave background.

Oct 4, 2026

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