A statistically significant (99.1%) excess of red galaxies from the APM Sky Catalogue is found around a sample of z ∼ 1 1Jy radio sources. The most plausible explanation for this result seems to be the magnification bias caused by the weak gravitational lensing of large scale structures at intermediate redshifts.

The propagation of light in an inhomogeneous universe is a long standing problem. Its resolution requires, first, a realistic description of the geometry of a clumpy universe and, second, solutions to the null geodesic equations given the metric of such a universe. The Friedmann-Robertson-Walker metric has become the standard description of the large scale geometry of the universe. However, the observable universe today is manifestly inhomogeneous. The weakly perturbed Friedmann-Robertson-Walker metric is often used to describe such a universe. But its validity is only guaranteed for a weakly inhomogeneous universe, where, for instance, overdensities are small , which is not true for sufficiently small scales in the universe today. It is well known, however, that the metric perturbations can still be small even if the overdensity is not small, given the right conditions and coordinates. However, spatial gradients of metric perturbations are not necessarily small any more. Here we estimate whether the second-order corrections involving them can affect significantly the expansion of the universe or the light propagation in it.

We have analyzed the effects of both large-scale inhomogeneities in the mass distribution and cosmological gravitational waves upon the time delay between two images in a gravitational lens system. We have shown that their leading order effect, which could potentially bias the determination of the Hubble parameter, is indistinguishable from a change in the relative angle between the source and the lens axis. Since the absolute angular position of the source is not directly measurable, nor does it enter the relationship between the Hubble parameter and the lens observables, the determination of Ho from gravitational lens time delays follows in the usual way, as if the metric perturbations were absent.

We have investigated multiple gravitational lensing by numerical “ray tracing” simulations. We have found that the distance between rays grows exponentially, on average, until it reaches the projected mean separation of lensing objects (∼ RV–1/2, where R is the system size and N is the number of scattering object). This nature may affect observations of high redshift objects or the anisotropy of the cosmic background radiation.

We investigated smoothing of the cosmic background radiation (CBR) by multiple gravitational lensing. The CBR is gravitationally scattered by galaxies, clusters of galaxies, and superclusters during the travel from the last scattering surface. Although the effect of the gravitational lensing was thought to be unimportant, we found that the multiple gravitational lensing by clusters of galaxies or by superclusters can reduced by a large factor. This result is explained by the fact that the distance between two light rays grows exponentially though multiple gravitational lensing. If such structures were formed at z = 2–5 and contain a large fraction of the mass of the universe (Ωs > 0.5), then multiple gravitational lensing can reduce the temperature anisotropy of the CBR by 40-60%, approximately up to a degree scale.

A wealth of observational data supports the commonly held view that damped Lyman-α (Lyα) absorption in QSO spectra is associated with neutral-hydrogen (HI) disks in spiral galaxies. Most of the HI probed by QSO absorption lines is traced by damped Lyα lines because of their high column densities, N > 1020 cm–2. The spiral galaxies hosting the HI disks can act as gravitational lenses on the QSOs. If the HI column density increases towards the center of the disks, as suggested by observations of local galaxies, the magnification bias preferentially selects for high column-density systems. The estimates of HI in damped Lyα systems can then systematically be distorted by gravitational lensing.

We study the influence of gravitational lensing on determinationing the number density and column density distributions of damped Ly-α systems.

We obtained 1.2 Å resolution spectra over the range 3175–7575 Å for the two components of the gravitational lens candidate HE 1104–1805 (z = 2.31, mB = 16.7 and 18.6, separation = 3.0 arcsec; cf. Wisotzki et al. 1993), with the aim of setting limits on the sizes of the clouds producing the Ly-α, C IV, and Mg II absorption systems. We refer to Smette et al. (1995) for a detailed account of this study.

We observed a common high-column density Ly-α absorption line in the spectra of both Q 1429–008 A & B, but with different equivalent widths.

Using high resolution spectral data of the Ly α forest, we found evidence for clustering of Ly α absorbers on scales of 8-10h0–1 Mpc.

Weak gravitational lensing can provide a direct measure of mass overdensity on scales of kpc to several Mpc. The total mass and light distribution in a survey of 32 clusters of galaxies is reviewed. The mass is derived from apodized inversion of thousands of weak lensing arclets in deep CCD shift-and-stare exposures to uniform faint surface brightness in two colors. Rest frame V band mass-to-light ratios of several hundred h solar are found.

The gravitational lensing of faint background galaxies by rich clusters is emerging as a very efficient method both to constrain the mass distribution of clusters of galaxies and to probe the statistical properties of faint background galaxies. We review results concerning the cores of cluster lenses, where recent Hubble Space Telescope (HST) images are giving new insights into the gravitational distortion phenomena.

We discuss HST imaging of eight spectroscopically-confirmed giant arcs, pairs and arclets. Although our HST observations include both pre- and post-refurbishment images, the depth of the exposures guarantees that the majority of the arcs are detected with diffraction-limited resolution. We present the size information on these distant field galaxies in the light of HST studies of lower redshift samples. We suggest that the dominant population of star-forming galaxies at z ∼ 1 is a factor of 1.5–2 times smaller in size than the equivalent population in the local field. This implies either a considerable evolution in the sizes of star-forming galaxies within the last ∼10 Gyrs or a shift in the relative space densities of massive and dwarf star-forming systems over the same time scale.

We report the discovery of a bright, arc-like feature with a redshift of z= 0.073 associated with the nearby cluster of galaxies ACO3408, at z = 0.042. The redshift, position, and geometry of the arc with respect to the central cD galaxy of the cluster strongly suggest that this is by far the nearest case known of gravitational lensing of a faint background galaxy.

We present preliminary results of a weak lensing investigation of the z = 0.43 cluster MS0302+1658.

We show the reconstructed mass distribution of the cluster CL0939+4713 (zd = 0.4) using data obtained with the WFPC2 instrument on HST. We find a remarkable correlation with the light distribution of the bright galaxies, which are probably cluster member galaxies. A bootstrapping analysis confirms this correlation, whereas an anti-correlation between the mass distribution and the faint galaxies - used for the mass reconstruction - is found. We give lower bounds on the mass inside the data field, and confirm that this cluster is indeed quite massive.

This paper is intended as an introduction to the theory of weak lensing. A review of the inversion formula introduced by Kaiser and Squires is presented. We then prove the formula of the aperture densitometry method in a simple way that allows a clear understanding of where the various terms come from. This is particularly useful to measure quantitatively masses in any region of a lens. We then summarize what has been learned from observations of strong lensing about the dark matter distribution; weak lensing should provide similar information on larger scales in clusters of galaxies.

I will review the basic principles and some of the most recent developments of parameter-free reconstructions of cluster mass profiles from the distortions of background galaxy images.

The possibility to reconstruct cluster mass distributions from their gravitational lensing effects on background sources is now firmly established and is discussed in a number of other contributions to these proceedings. Here, we want to suggest a new method, the parallax method (Bartelmann & Narayan 1995), to infer the redshifts of the background sources, which are in general too faint to allow spectroscopy. The method is based on gravitational lensing, and apart from arclet redshifts it yields calibrated, accurate cluster reconstructions. The key idea is simple and rests on three facts: (1) The strength of lensing effects increases with source redshift, if the redshift is kept fixed. (2) The surface brightness of the arclet sources steeply decreases with redshift z. Neglecting spectral effects, the surface brightness is ∝ (1 + z)−4. (3) The surface brightness of the sources is invariant to lensing. In combination, these facts imply that lensing effects become stronger with decreasing surface brightness, so that relative distances of arclet sources can be inferred from the variation of lensing effects with the surface brightness of lensed sources. If the redshift of the brightest sources can be measured spectroscopically, the relative distances can be calibrated and the average redshift as a function of surface brightness can be found.

The shear distortion of galaxies behind a large cluster provides us with only a relative measure of the mass of the cluster (Tyson et al. 1990, Kaiser & Squires 1993) due the invariance of shear to a sheet of matter. Thus we can at best only place lower limits on cluster masses, with the constraint that the surface density, κ(θ)=Σ(θ)/Σc, is non-negative. However, an absolute measurement of the mass can be obtained via the magnification of background galaxies (Broadhurst, Taylor & Peacock 1995, hereafter BTP). Here we describe the magnification effect, its observational consequences and mass reconstruction in the linear and nonlinear regimes. We also describe a number of applications in progress.