Weak gravitational lensing is an ecient technique for detecting galaxy clusters and probing their mass distribution. We present a weak gravitational lensing analysis of a large sample of galaxy clusters. We have built a nearly complete sample of 50 optically rich clusters, located in the redshift range 0:1 < z < 0:6 and observed in the Canada France Hawaii Telescope Legacy Survey (CFHT-LS). We used weak gravitational lensing to measure, for each galaxy cluster, the density radial prole, the total mass and the mass-to-light ratio (by comparing with the total luminosity of the member galaxies). This project is a preliminary step towards the next analysis of the weak lensing galaxy clusters in the surveys KiDS and VOICE, which are currently collecting data with the VLT Survey Telescope, in Chile.

On the formulation frameworks of linearly perturbed spacetime and weak gravitational lensing(WGL) we studied the statistical properties of a bundle of light rays propagating through stochastic gravitational wave background(SGWB). For this we considered the SGWB as tensor perturbations of linearly perturbed Friedmann spacetime. Using the solution of null geodesic deviation equation(NGDE) we related the convergence, shear and rotation deformation spectra of WGL with the strain spectra of SGWB. Adopting the astrophysical and cosmological SGWB strain spectra which were already known we investigated the approximated spectral forms of convergence, shear and rotation of WGL.

Quasars at cosmological distances can be gravitationally lensed by galaxies into two or more images. The probability of this lensing and the angular separation between the images depend on the geometry and the expansion history of the universe as well as the lensing galaxies. The time delay between lensed images is also a direct indicator of the size of the universe. I review these cosmological applications of multiple-image gravitationally lensed quasars to determine or constrain the cosmological parameters.

The lens mass determined from the photometrically obtained Einstein time scale suffers from large uncertainty due to the lens parameter degeneracy. The uncertainty can be substantially reduced if the mass is determined from the lens proper motion obtained from astrometric measurements of the source image centroid shifts, δθc δθc , by using high precision interferometers from space-based platform such as the Space Interferometry Mission (SIM), and ground-based interferometers soon available on several 8-10m class telescopes. However, for the complete resolution of the lens parameter degeneracy it is required to determine the lens parallax by measuring the parallax-induced deviations in the centroid shifts trajectory, Δδθc Δδθc aloe. In this paper, we investigate the detectabilities of δθc δθc and Δδθc Δδθc by determining the distributions of the maximum centroid shifts, f(δθc,max) f(δθc,max) , and the average maximum deviations, (<Δδc,max>) (<Δδc,max>) , for different types of Galactic microlensing events caused by various masses. From this investigation, we find that as long as source stars are bright enough for astrometric observations it is expected that f(δθc) f(δθc) for most events caused by lenses with masses greater than 0.1 M⨀ M⨀ regardless of the event types can be easily detected from observations by using not only the SIM (with a detection threshold but also the δθth\~3μas) δθth\~3μas) but also the ground-based interferometers (withδθth\~3μas) (withδθth\~3μas) . However, from ground-based observations, it will be difficult to detect Δδθc Δδθc for most Galactic bulge self-lensing events, and the detection will be restricted only for small fractions of disk-bulge and halo-LMC events for which the deviations are relatively large. From observations by using the SIM, on the other hand, detecting Δδθc Δδθc will be possible for majority of disk and halo events and for a substantial fraction of bulge self-lensing events. For the complete resolution of the lens parameter degeneracy, therefore, SIM observations will be essential.

The role of gravitational lenses as valuable tools for astrophysics and cosmology is highlighted.

To examine the effect of neighboring galaxies on the gravitational lensing statistics, we performed numerical simulations of lensing by many galaxies. The models consist of a galaxy in the rich cluster like Coma, or a galaxy surrounded by field galaxies in Ω0 = 1 universe with Ωgal = 0.1, Ωgal = 0.3 or Ωgal=1.0, Ωgal is the total mass in galaxies. Field galaxies either have the same mass or follow Schechter luminosity function and luminosity-velocity relation. Each lensing galaxy is assumed to be singular isothermal sphere (SIS) with finite cutoff radius. In most simulations, the lensing is mainly due to the single galaxy. But in Ωgal = 0.3 universe, one out of five simulations have 'collective lensing' event in which more than two galaxies collectively produce multiple images. These cases cannot be incorporated into the simple 'standard' lensing statistics calculations. In cases where 'collective lensing' does not occur, distribution of image separation changes from delta function to bimodal distribution due to shear induced by the surrounding galaxies. The amount of spread in the distribution is from a few % up to ~50% of the mean image separation in case when the galaxy is in the Coma-like cluster or when the galaxy is in the field with Ωgal = 0.1 or Ωgal=0.3. The mean of the image separation changes less than 5% compared with a single lens case. Cross section for multiple image lensing turns out to be relatively insensitive to the presence of the neighboring galaxies, changing less than 5% for Coma-like cluster and Ωgal=0.1, 0.3 universe cases. So we conclude that Coma-like cluster or field galaxies whose total mass density Ωgal < 0.3 do not significantly affect the probability of multiple image lensing if we exclude the 'collective lensing' cases. However, the distribution of the image separations can be significantly affected especially if the 'collective lensing' cases are included. Therefore, the effects of surrounding galaxies may not be negligible when statistics of lensing is used to deduce the cosmological informations.

To extend the work of Gott, Park, and Lee (1989), statistical properties of gravitational lensing in a wide variety of cosmological models involving non-zero cosmological constant is investigated, using the redshifts of both lens and source and observed angular separation of images for gravitational lens systems. We assume singular isothermal sphere as lensing galaxy in homogenous and isotropic Friedmann­Lemaitre-Robertson- Walker universe, Schechter luminosity function, standard angular diameter distance formula and other galaxy parameters used in Fukugita and Turner (1991). To find the most adequate flat cosmological model and put a limit on the value of dimensionless cosmological constant ⋋0, the mean value of the angular separation of images, probability distribution of angular separation and cumulative probability are calculated for given source and lens redshifts and compared with the observed values through several statistical methods. When there is no angular selection effect, models with highest value of ⋋0 is preferred generally. When the angular selection effects are considered, the preferred model depends on the shape of the selection functions and statistical methods; yet, models with large ⋋0 are preferred in general. However, the present data can not rule out any of the flat universe models with enough confidence. This approach can potentially select out best model. But at the moment, we need more data.

The most favourable possibilities to observe the phenomena of gravitational lensing are the high amplification events and the time delay between the images. These effects provide us the information to determine the Hubble parameter and the matter distribution in the universe. The image properties due to micro-lensing also is of an importance to find out the size and the structure of the source.