We perform a measurement of the mass-richness relation of the redMaPPer galaxy cluster catalogue using weak lensing data from the Sloan Digital Sky Survey (SDSS). We have carefully characterized a broad range of systematic uncertainties, including shear calibration errors, photo-z biases, dilution by member galaxies, source obscuration, magnification bias, incorrect assumptions about cluster mass profiles, cluster centring, halo triaxiality and projection effects. We also compare measurements of the lensing signal from two independently produced shear and photometric redshift catalogues to characterize systematic errors in the lensing signal itself. Using a sample of 5570 clusters from 0.1 <= z <= 0.33, the normalization of our power-law mass versus. relation is log(10)[M-200m/ h-M-1(circle dot)] = 14.344 +/- 0.021 (statistical) +/- 0.023 (systematic) at a richness lambda= 40, a 7 per cent calibration uncertainty, with a power-law index of 1.33(- 0.10)(+0.09) (1 sigma). The detailed systematics characterization in this work renders it the definitive weak lensing mass calibration for SDSS redMaPPer clusters at this time.

Cosmological constraints from galaxy surveys are as accurate as our understanding of the relative distributions of dark matter and galaxies, known as galaxy bias. Weak gravitational lensing is a powerful probe of galaxy bias, since the distortion in the shapes of distant galaxies, called shear, is directly related to the dark matter distribution, which can be compared to the galaxy field. I look at the galaxy clustering amplitude relative to the dark matter field, quantified by the galaxy bias b, as well as the cross-correlation coefficient r, which tells us how correlated the positions of galaxies are with the dark matter. In this thesis I present several techniques to constrain galaxy bias through weak lensing, using both numerical simulations and observational data. The most commonly used method, using aperture statistics, is shown to be subject to serious systematics in the presence of noisy data and scale- and time dependence in the galaxy bias. A local comparison technique is introduced, where the foreground distribution is used to predict the shear in the background, to which it is compared. The technique is tested with simulations, concluding that it requires high quality data. A model fitting approach is proposed, based on the McDonald (2006) galaxy bias model. The two parameters of this model, a large scale bias, b1, and a parameter, b2, that quantifies the scale dependence of the bias, are insufficient in the presence of stochasticity. Therefore, R is introduced as an additional parameter to take this into account. I present galaxy bias constraints for two spectroscopic galaxy samples: the Baryon Oscillations Spectroscopic Survey (BOSS) and the WiggleZ Dark Energy Survey (WiggleZ), applying the traditional aperture method and the model fitting approach to the Red Sequence Cluster Lensing Survey (RCSLenS). Both techniques strongly suggest that galaxies trace mass, but in a complicated way, with differences in scale- and time dependence between the samples considered. The WiggleZ galaxy bias is found to be around b ~ 1:2, depending on redshift and scale, and has a low cross-correlation coefficient of r ~ 0:5 at small scales. The BOSS samples have higher bias with scale dependence around b ~ 2:0 and show no sign of stochasticity, finding r to be close enough to unity to be explained within a deterministic scenario. The observations are in line with previous galaxy bias measurements from lensing data. The thesis incorporates work on the X-ray Luminosity Function (XLF) of galaxy clusters, measured from the Wide Angle ROSAT Pointed Survey (WARPS). Evolution is quantified with a likelihood analysis and I conclude that it is driven by a decreasing number density of high luminosity clusters with redshift, while the bulk of the cluster population remains nearly unchanged out to redshift z ~ 1:1, as expected in a low density Universe. I conclude by investigating the impact of my galaxy bias measurements from BOSS and WiggleZ on the growth rate of structure, as extracted from Redshift Space Distortions (RSD). The imperfect correlation between the galaxy and matter field, as quantified by R and b2, leads to an underestimation of the true growth rate under the assumption of a linear bias. Therefore, in order to constrain galaxy bias and gravity simultaneously, future cosmological redshift surveys require high quality lensing data.

With a large, unique spectroscopic survey in the fields of 28 galaxy-scale strong gravitational lenses, we identify groups of galaxies in the 26 adequately sampled fields. Using a group-finding algorithm, we find 210 groups with at least 5 member galaxies; the median number of members is 8. Our sample spans redshifts of 0.04 <= z(grp) <= 0.76 with a median of 0.31, including 174 groups with 0.1 < z(grp) < 0.6 The groups have radial velocity dispersions of 60 <= sigma(grp) <= 1200 km s(-1) with a median of 350 km s(-1). We also discover a supergroup in field B0712+472 at z = 0.29 that consists of three main groups. We recover groups similar to similar to 85% of those previously reported in these fields within our redshift range of sensitivity and find 187 new groups with at least five members. The properties of our group catalog, specifically, (1) the distribution of sgrp, (2) the fraction of all sample galaxies that are group members, and (3) the fraction of groups with significant substructure, are consistent with those for other catalogs. The distribution of group virial masses agrees well with theoretical expectations. Of the lens galaxies, 12 of 26 (46%) (B1422+231, B1600+434, B2114+022, FBQS J0951+2635, HE0435-1223, HST J14113+5211, MG0751+2716, MGJ1654+1346, PG 1115+080, Q ER 0047-2808, RXJ1131-1231, and WFI J2033-4723) are members of groups with at least five galaxies, and one more (B0712+472) belongs to an additional, visually identified group candidate. There are groups not associated with the lens that still are likely to affect the lens model; in six of 25 (24%) fields (excluding the supergroup), there is at least one massive (sigma(grp) >= 500 km s(-1)) group or group candidate projected within 2' of the lens.

Weak gravitational lensing is now well established as a powerful cosmological probe, particularly for studying large scale structure growth in the Universe. The vast majority of weak lensing experiments to date use optical and near infrared observations which are well suited to the requirements in source densities and shape analysis. In this thesis we outline the prospects associated with weak lensing surveys from radio observations. This can offer key advantages to optical counterpart studies such as the well defined observing beam pattern of a radio telescope and a window into a much broader observed redshift distribution. In addition to the prospect of radio weak lensing surveys alone, combining with optical counterparts in a cross-correlation study has been shown to mitigate uncorrelated systematics, further motivating the case for radio based weak lensing studies. The correlation of galaxy shapes through multi-wavelength observations will affect the noise on the cosmological power spectrum in cross-correlation analysis. We use radio and optical observations of the COSMOS field with the VLA and HST respectively, accompanied with simulations for calibration in order to measure shape correlations between wavelength regimes. Although we do not detect a correlation between optical and radio shapes, a lower limit on the intrinsic astrophysical scatter was placed at >0.212pi (or 38.2 degrees), through a Monte Carlo simulation of source catalogues with the measured uncertainties. The SuperCLASS experiment aims to measure a weak lensing signal with radio observations from a super-cluster field. We introduce the radio data, collected with the e-MERLIN and JVLA, and the reduction steps taken. Assisted by simulations, we have designed a shape measurement pipeline (SuperTRAP) which performs additional phase rotation and averaging steps to extract visibility sets on a source by source basis followed by image plane shape analysis. A series of staged tests of increasing complexity are outlined here and evaluated by the shape recovery bias and efficiency. Finally we present the optical counterpart observations and shape analysis for the SuperCLASS field, with data collected by the Subaru Suprime-Cam. Observational systematics are measured to form representative PSF models in each CCD exposure and the subsequent shape analysis from the I band photometry is presented. Shear analysis from the measured power spectrum shows good agreement with theoretical predictions. From the measured shear power spectrum we detect a strong signal in the E-mode band powers, equivalent to a 9.31sigma detection. Our measurements from the B-mode and E-B cross band powers suggest negligible contamination from systematics. The optical analysis presented here will provide the counterpart analysis to the radio for future cross-correlation studies.

Observations of gravitationally microlensed quasars offer a unique opportunity to probe quasar structure on extremely small scales. In this thesis, we conduct extensive microlensing simulations and compare with observational data to constrain quasar accretion discs, and conduct preliminary probes of broad emission line region structure. This analysis is done using a new single-epoch imaging technique that requires very little telescope time, and yet produces results that are comparable to those obtained from long-term monitoring campaigns. / We begin by exploring the impact of variable smooth matter percentage and source size on microlensing simulations. Adding a smooth matter component affects minimum and saddle point images differently, broadening the magnification distribution for the saddle point image significantly. However, increasing the radius of the background source washes out this difference. The observation of suppressed saddle point images can therefore only be explained by microlensing with a smooth matter component if the background source is sufficiently small. We use these simulations, in combination with I-band imaging of the lensed quasar MG 0414+0534 to constrain the radius of the quasar source. This demonstrates the viability of a single-epoch imaging method for constraining quasar structure. / This technique is then expanded to single-epoch multi-band observations, in order to constrain the radial profile of quasar accretion discs as a function of observed wavelength. We present new Magellan observations of two gravitationally lensed quasars: MG 0414+0534 and SDSS J0924+0219. We also analyse two epochs of Q2237+0305 data obtained from the literature. Our results are compared with four fidicial accretion disc models. At the 95 per cent level, only SDSS J0924+0219 is inconsistent with any of the accretion disc models. When we combine the results from all three quasars -- a first step towards assembling a statistical sample -- we find that the two steepest accretion disc models are ruled out with 68 per cent confidence. / In addition, we are also able to use our microlensing simulations to constrain the smooth matter percentages in the lenses at the image positions. In both MG 0414+0534 and SDSS J0924+0219 we find smooth matter percentages that are inconsistent with zero. A smooth matter percentage of approximately 50 per cent is preferred in MG 0414+0534, and approximately 80 per cent in SDSS J0924+0219. Q2237+0305 is usually assumed to have a smooth matter percentage of zero at the image positions, as they lie in the bulge of the lensing galaxy. Though our measurement is consistent with a zero smooth matter percentage, there is a peak in the probability distribution at a value 20 per cent. This is perhaps a hint of additional intervening structures along the line of sight to the background quasar. / We test the sensitivity of our accretion disc constraints to a range of modelling parameters. These include errors in lens modelling, Bayesian prior probability selection, errors in observational data, and the microlens mass function. Constraints on the power-law index relating source radius to observed wavelength are found to be relatively unaffected by changes in the modelling parameters. Constraints on source radii are found to be more strongly affected. / Finally, the broad emission line region of Q2237+0305 is examined. Gemini IFU observations are presented clearly showing differential microlensing across the velocity profile of the CIII] emission line. To analyse this signature, we present three simple broad emission line region models: a biconical outflow, a Keplerian disc, and spherical infall. A method is developed to compare the shapes of simulated flux ratio spectra with the observed spectrum. We are unable to discriminate between the biconical outflow and Keplerian disc models when we average over all viewing angles and orientations. The spherical infall model, however, does not fit the observed data. We also find that for the non-spherically symmetric geometries, low inclination angles are essentially incompatible with the observations. This analysis offers hope that with sufficiently high signal-to-noise observations, differential microlensing signatures may allow us to constrain the geometry and kinematics of this poorly understood portion of quasar structure.

Gravitational lensing, initially a phenomenon used as a solid confirmation of General Relativity, has defined itself in the past decade as a standard astrophysical tool. The ability of a lensing system to produce multiple images of a luminous source is one of the aspects of gravitational lensing that is exploited both theoretically and observationally to improve our understanding of the Universe. In this thesis, within the field of multiple imaging we explore the case of maximal lensing, that is, the configurations and conditions under which a set of deflecting masses can produce the maximum number of images of a distant luminous source, as well as a study of the value for this maximum number itself. We study the case of a symmetric distribution of n-1 point-mass lenses at the vertices of a regular polygon of n-1 sides. By the addition of a perturbation in the form of an n-th mass at the center of the polygon it is proven that, as long as the mass is small enough, the system is a maximal lensing configuration that produces 5(n-1) images. Using the explicit value for the upper bound on the central mass that leads to maximal lensing, we illustrate how this result can be used to find and constrain the mass of planets or brown dwarfs in multiple star systems. For the case of more realistic mass distributions, we prove that when a point-mass is replaced with a distributed lens that does not overlap with existing images or lensing objects, an additional image is formed within the distributed mass while positions and numbers of existing images are left unchanged. This is then used to conclude that the maximum number of images that n isolated distributed lenses can produce is 6(n-1)+1. In order to explore the likelihood of observational verification, we analyze the stability properties of the symmetric maximal lensing configurations. Finally, for the cases of n=4, 5, and 6 point-mass lenses, we study asymmetric maximal lensing configurations and compare their stability properties against the symmetric case.

Gravitational lensing, initially a phenomenon used as a solid confirmation of General Relativity, has defined itself in the past decade as a standard astrophysical tool. The ability of a lensing system to produce multiple images of a luminous source is one of the aspects of gravitational lensing that is exploited both theoretically and observationally to improve our understanding of the Universe. In this thesis, within the field of multiple imaging we explore the case of maximal lensing, that is, the configurations and conditions under which a set of deflecting masses can produce the maximum number of images of a distant luminous source, as well as a study of the value for this maximum number itself. We study the case of a symmetric distribution of n-1 point-mass lenses at the vertices of a regular polygon of n-1 sides. By the addition of a perturbation in the form of an n-th mass at the center of the polygon it is proven that, as long as the mass is small enough, the system is a maximal lensing configuration that produces 5(n-1) images. Using the explicit value for the upper bound on the central mass that leads to maximal lensing, we illustrate how this result can be used to find and constrain the mass of planets or brown dwarfs in multiple star systems. For the case of more realistic mass distributions, we prove that when a point-mass is replaced with a distributed lens that does not overlap with existing images or lensing objects, an additional image is formed within the distributed mass while positions and numbers of existing images are left unchanged. This is then used to conclude that the maximum number of images that n isolated distributed lenses can produce is 6(n-1)+1. In order to explore the likelihood of observational verification, we analyze the stability properties of the symmetric maximal lensing configurations. Finally, for the cases of n=4, 5, and 6 point-mass lenses, we study asymmetric maximal lensing configurations and compare their stability properties against the symmetric case.

In this thesis, I explore how the environments of both galaxy and cluster-scale strong gravitational lenses affect studies of cosmology and the properties of the earliest galaxies. Galaxy-scale lenses with measured time delays can be used to determine the Hubble constant, given an accurate lens model. However, perturbations from structures along the line of sight can introduce errors into the measurement. I use data from a survey towards known lenses in group environments to calculate the external shear in these systems, which is typically marginalized over in standard lens analyses. In three of six systems where I compare the independently-calculated environment shear to lens model shears, the quantities disagree at greater than 95% confidence. We explore possible sources of this disagreement. Using these data, I generate fiducial lines of sight and insert mock lenses with assumed input physical and cosmological parameters and find that those parameters can be recovered with ∼ 5-10% scatter when uncertainties in my characterization of the environment are applied. The lenses in groups have larger bias and scatter. I predict how well new time delay lenses from LSST will constrain H₀ and find that an ensemble of 500 quad lenses will recover H₀ with ∼ 2% bias with ∼ 0.3% precision. On larger scales, galaxy cluster lenses can magnify the earliest galaxies into detectability. While past studies have focused on single massive clusters, I investigate the properties of lines of sight, or "beams", containing multiple cluster-scale halos in projection. Even for beams of similar total mass, those with multiple halos have higher lensing cross sections on average. The optimal configurations for maximizing the cross section are also those that maximize faint z ∼ 10 detections. I present a new selection technique to identify beams in wide-area photometric surveys that contain high total masses and often multiple clusters in projection as traced by luminous red galaxies. I apply this technique to the Sloan Digital Sky Survey and present the 200 most promising beams. Several are confirmed spectroscopically to be among the highest mass beams known with some containing multiple clusters. These are among the best fields to search for faint high-redshift galaxies.

Weak gravitational lensing is a powerful astronomical tool for constraining cosmological parameters that is entering its prime. Lensing occurs because gravitational fields deflect light rays and measuring this deflection through a statistic known as cosmic shear allows us to directly measure the properties of dark matter and dark energy on large scales. In principle, gravitational lensing is a clean probe of the cosmology of the Universe, as it depends on gravity alone and not on incomplete astrophysical models or approximations. In practice, however, there are several factors that limit the accuracy and precision of lensing measurements. These include accurate measurement of galaxy shapes, correctly accounting for distortions to galaxy images due to the point spread function of the telescope, the presence of intrinsic alignments (IAs) of galaxy shapes due to physical processes, and inaccuracies in commonly-used galaxy photometric redshift information. These effects may all introduce systematic errors in lensing measurements which must be carefully accounted for to ensure that cosmological constraints from lensing are unbiased and as precise as possible. The Canada-France-Hawaii-Telescope Lensing Survey (CFHTLenS) is the largest weak lensing survey completed to date, covering 154 square degrees of the sky in 5 optical bands, with photometric redshift information for every survey galaxy. With lensing measurements from more galaxies than ever before, the statistical uncertainties on parameter estimates will be the lowest ever achieved from weak lensing. If left unaccounted for, sources of systematic error would dominate over the statistical uncertainty, potentially biasing parameter estimates catastrophically. A technique known as tomography in which galaxies are sorted into bins based on their redshift can help constrain cosmological parameters more precisely. This is because utilising the redshifts of survey galaxies retains cosmological information that would otherwise be lost, such as the behaviour of dark energy and the growth of structure over time. Tomography, however, increases the demand for systematics-free galaxy catalogues as the technique is strongly sensitive to the IA signal and photometric redshift errors. Therefore, future lensing analyses will require a more sophisticated treatment of these effects to extract maximal information from the lensing signal. A thorough understanding of the error on lensing measurements is necessary in order to produce meaningful cosmological constraints. One of the key features of cosmic shear is that it is highly correlated over di erent angular scales, meaning that error estimates must take into account the covariance of the data over different angular scales, and in the case of tomography, between different redshift bins. The behaviour and size of the (inverse) covariance matrix is one of the limiting factors in such a cosmological likelihood analysis, so constructing an accurate, unbiased estimate of the covariance matrix inverse is essential to cosmic shear analysis. This thesis presents work to optimise tomographic weak lensing analysis and achieve the tightest parameter constraints possible for a CFHTLenS-like survey. N-body simulations and Gaussian shear fields incorporating an IA model (known as the `non-linear alignment' model) with a free parameter are used to estimate fully tomographic covariance matrices of cosmic shear for CFHTLenS. We simultaneously incorporate for the first time the error contribution expected from the non-linear alignment model for IAs and realistic photometric redshift uncertainties as measured from the CFHTLenS. We find that non-Gaussian simulations that incorporate nonlinearity on small scales are needed to ensure the covariance is not underestimated, and that the covariance matrix is shot-noise dominated for almost all tomographic correlations. The number of realisations of the simulations used to estimate the covariance places a hard limit on the maximum number of tomographic bins that one can use in an analysis. Given the available number of lines of sight generated from CFHTLenS-like simulations, we find that up to ~ 15 tomographic bins may be utilised in a likelihood analysis. The estimated tomographic covariance matrices are used in a least-squares likelihood analysis in order to find the combination of both angular and tomographic bins that gives the tightest constraints on some key cosmological parameters. We find that the optimum binning is somewhat degenerate, with around 6 tomographic and 8 angular bins being optimal, and limited by the available number of realisations of the simulations used to estimate the covariance. We also investigate the bias on best- t parameter estimates that occurs if IAs or photometric redshift errors are neglected. With our choice of IA model, the effect of neglecting IAs on the best- t cosmological parameters is not significant for a CFHTLenS-like survey, although this may not be true if the IA signal differs substantially from the model, or for future wide-field surveys with much smaller statistical uncertainties. Similarly, neglecting photometric redshift errors does not result in significant bias, although we apply similar caveats. Finally, we apply the results of this optimisation to the CFHTLenS cosmic shear data, performing a preliminary analysis of the shear correlation function to produce both 2D and optimal tomographic cosmological constraints. From 6-bin tomography, we constrain the matter density parameter Ωm = 0:419+0:123-0:090, the amplitude of the matter power spectrum σ8 = 0:623+0:101 -0:084 and the amplitude parameter of the non-linear alignment model, A = -1:161+1:163 -0:597. We perform this analysis to test the validity and limitations of the optimal binning on real data and find that 6-bin tomography improves parameter constraints considerably, albeit not as much as when performed on simulated data. This analysis represents an important step in the development of techniques to optimise the recovery of lensing information and hence cosmological constraints, while simultaneously accounting for potential sources of bias in shear analysis.

This thesis describes an investigation into weak gravitational lensing, a unique and powerful astronomical tool for the study of dark matter on large scales. Lensing distorts background images, inducing correlations in the observed ellipticities of galaxies, and these correlations can be used to estimate many characteristics of the Universe. Key to all weak lensing studies is a reliable and unbiased method to detect weak lensing distortions from observed galaxy images that are contaminated by Earth and telescope-based shearing and smearing distortions. A new galaxy model-fitting technique is presented that has been developed in order to satisfy this requirement, which will also permit future signal-to-noise optimised measurements of weak lensing shear. Model-fitting provides a good alternative to the standard scite{KSB} method (KSB), and comparisons between the two techniques are drawn from an analysis of deep {it R} band imaging from the COMBO-17 survey, revealing strong evidence for the presence of bias in KSB galaxy shape measurement. With the galaxy model-fitting technique, an investigation into the effectiveness of the Oxford Dartmouth Thirty degree survey (ODT) for gravitational lensing studies is presented, resulting in the detection of weak gravitational lensing by large scale structure, or `cosmic shear', in 0.7 square degrees of the best seeing ODT images. One concern for all cosmic shear studies is that the weak lensing signal, manifest in the weakly correlated ellipticities of distant galaxies, is contaminated by the intrinsic alignment of close galaxy pairs, potentially induced during galaxy formation by physical interactions such as tidal forces. This contamination is investigated theoretically, through numerical simulations, and observationally, with an analysis of the COMBO-17 survey and the study of published results from the Red-sequence Cluster survey and the VIRMOS-DESCART survey, concluding that the intrinsic alignment effect is at the lower end of the range of theoretical predictions. The impact of intrinsic galaxy alignments on cosmological parameter estimation is investigated, with an analysis of the weak lensing results from the COMBO-17 survey. When marginalising over the observationally constrained intrinsic alignment signal, the amplitude of the matter power spectrum sigma_8 is reduced by ~0.03 to sigma_8(Omega_m / 0.27)^{0.6} = 0.71 pm 0.11, where Omega_m is the matter density parameter. With distance information from either spectroscopy or photometric redshifts, the down-weighting of nearby galaxy pairs in weak lensing analysis can be optimised to virtually eliminate the systematic errors in the shear signal arising from intrinsic galaxy alignments, leaving a much smaller, largely statistical error. This method is applied to the photometric redshift sample of the COMBO-17 survey. Weak lensing measurements from the forthcoming SuperNova/Acceleration Probe weak lensing survey (SNAP), and the Canada-France-Hawaii Telescope Legacy survey, are expected to be contaminated on scales >1 arcminute by intrinsic alignments at the level of ~ 1% and ~2% respectively. Division of the SNAP survey for lensing tomography significantly increases the contamination in the lowest redshift bin to ~7% and possibly higher. Removal of the intrinsic alignment effect by the downweighting of nearby galaxy pairs will therefore be vital for the lensing tomography studies of SNAP.