The statistics of gravitationally lensed quasars requires that λ < 0.7 at 90% confidence. This limit is weakly affected by the evolution of galaxies through merging. If E/S0 galaxies have much higher dust opacities at redshifts of 0.5-1.0 than they do locally, these limits can be evaded.

Quantitative estimates of lensing probabilities must be self-consistent. In particular, for asymptotically isothermal models: (1) using the (3/2)1/2 correction for the velocity dispersion overestimates the expected number of lenses by 150% and their average separations by 50%, thereby introducing large cosmological errors; (2) when a core radius is added to the SIS model, the velocity dispersion must be increased; and (3) cross sections and magnification bias cannot be separated when computing the lensing probability. When we self-consistently calculate the effects of finite core radii in flat cosmological models, we find that the cosmological limits are independent of the core radius.

The search for multiply imaged quasars among highly luminous quasars (HLQs) is a very good strategy to determine the fundamental parameters of the Universe. We report on the present observational status of a combined sample of HLQs, including new observations obtained with the Nordic Optical Telescope (NOT) and at ESO. This combined sample of HLQs now contains 1178 distinct HLQs. A complete list of the total sample will be soon made available, through a World-Wide-Web page. Preliminary maximum likelihood results are also presented, using a simple statistical model to constrain the values of galactic parameters, of the number counts of QSOs, and of the cosmological constant.

For gravitational lens systems with unknown lens redshifts, the redshifts and brightnesses of the lenses are predicted for a variety of cosmological models. Besides providing hints as to which systems should be observed with a realistic chance of measuring the lens redshifts, which are needed for detailed lensing statistics and for modelling the lenses, these calculations give a visual impression of the influence of the cosmological model in gravitational lensing.

We investigate the statistical properties of gravitational lenses for flat models in which a cosmological term decreases with time as ⁁ ∝ a−m, where a is the scale factor and m is a parameter (0 ≤ m < 3) (Bloomfield Torres and Waga 1995).

Many observations of large-scale and cosmological structures in the universe have been collected, but so far there is no consistent theoretical explanation. In the region within 100 Mpc from us, the observed two-point correlations of galaxies and clusters of galaxies can be described well by low-density homogeneous cosmological models (Bahcall & Cen 1993; Suto 1993). On the other hand, the observed anisotropies of the cosmic microwave background radiation have been explained well by comparatively high-density cosmological models such as the Einstein-de Sitter model (Bunn & Sugiyama 1994). In the intermediate scale, the angular sizes of the cores of quasars have been measured and their redshift dependence has been shown to be more consistent with the Einstein-de Sitter model than with the low-density models (Kellermann 1993). The number count-magnitude relation for remote galaxies supports low-density models with a nonzero cosmological constant (for example, Fukugita et al. 1990), but these models may be inconsistent with the observed distribution of Lyα clouds (Fukugita & Lahav 1991).

The current status on the value of the Hubble constant is reviewed with the emphasis given to the origin of the discrepancy among authors. I argue that the situation is not too controversial and straightforward reading of observations indicates a high value (H0 ≃ 75 km s−1 Mpc−1).

A time delay of 12±3 days has been measured for the lens system 0218+357 using VLA 15GHz polarization observations.

The gravitational lens 0957+561 has been monitored by our group for 16 years, using the VLA at 5 GHz. Since our last report in 1992, both images have returned to their quiescent flux levels, and the A image has brightened again. We apply various analysis methods to the light curves, and obtain a preliminary estimate of τ = 455 ± 40 days for the time delay.

The time delay in Q0957+561 remains indeterminate due to differences between statistical methods, irregular data spacings, and (possibly) microlensing.

The double quasar 0957+561 was the first discovered instance of multiple imaging via gravitational lensing. The galaxy cluster is an important deflector as well as the first ranked galaxy. This has so far precluded construction of a unique model of the lens, reducing the accuracy of the derived H0 value. We have obtained deep images of the system at CFHT. The cluster is sufficiently massive to cause distortions on distant background galaxy images. We have used a mass map derived from lensing distortions to improve the accuracy of the cluster center location and place new limits on H0.

The Q0957+561 time delay remains controversial, and we present four new time delay calculations based upon the intensively sampled data of the last three years.

We present our first results of a photometric monitoring project of the twin quasar 0957+561. This project aims mainly at the improvement of the determination of the time delay ΔT(A,B) for this gravitational lens, since the “time delay controversy on QSO 0957+561 (is) not yet decided” (Pelt et al. 1994). In addition, the quite large field of the CCD used allows also a long-term astrometric and photometric study of stars and galaxies in the field within a radius of about 10 arcminutes around the lens.

All the popular models for structure formation are based on three key ingredients: (a) a model for the background universe (b) some mechanism for generating small perturbations in the early universe and (c) specification of the nature of the dark matter.

Gravitational lensing provides a strict test of cosmogonic models. We use fully non-linear numerical propagation of light rays through a model universe with inhomogeneities derived from a particular cosmogonic model, i.e. three-dimensional lensing simulations, to study its lensing properties. As a first example we present results for the standard CDM scenario. The lensing test for this model predicts that we should have seen far more widely split quasar images than have been found.

There is still debate as to whether wide separation (Δθ ≳ 3″) double quasars are physical binaries or gravitationally lensed sources. We proceed under the assumption that most of these objects are the result of lensing, and use maximum likelihood techniques (Kochanek 1993) to infer information about the mass distribution of deflectors that would be required to produce these wide image separations. Under the above assumptions, the most consistent explanation is the existence of a significant population of dark objects with the mass of groups of galaxies.

Cosmological lens statistics was studied first by Turner, Ostriker, & Gott (1984), and developed by Hinshaw & Krauss (1987), Gott, Park, & Lee (1989), Turner (1990), Krauss & White (1992), and Wallington & Narayan (1993). The expected number of lensed quasars in general quasar catalogs was examined by Fukugita & Turner (1991), Kochanek (1991), and Fukugita et al. (1992), and the number expected in the HST Snapshot Survey (Bahcall et al. 1992, Maoz et al. 1992, 1993) was examined by Maoz & Rix (1939) and Kochanek (1993). In most of these studies, galaxies were assumed to be the lenses, and clusters of galaxies played only auxiliary roles. As a result, the expected number of lensed quasars with separations larger than 3 arcsec is negligibly small compared to the total number of lenses. However, about 33% of observed lensed quasars have image separations larger than 3 arcsec (Maoz et al. 1993, Refsdal & Surdej 1994). This observational fact is very important.

While the strategy for the first applications of weak lensing has been to “go deep” it is equally interesting to use one's telescope time to instead “go wide”. The Sloan Survey (SDSS) provides a natural framework for a very wide area weak lensing survey.

We are developing a wide-field CCD camera system which is optimized for using weak gravitational lensing to study the distribution of dark matter in clusters of galaxies and eventually the field. The system will be used at the Apache Point Observatory (APO) 3.5 meter telescope in New Mexico.