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This thesis presents a practical guide to applying shear measurements as a cosmological tool. We first present one of two science-ready galaxy shape catalogues from Year 1 of the Dark Energy Survey (DES Y1), which covers 1500 square degrees in four bands griz, with a median redshift of 0.59. We describe the shape measurement process implemented by the DES Y1 im3shape catalogue, which contains 21.9M high-quality r-band bulge/disc fits. In Chapter 3 a new suite of image simulations, referred to as hoopoe, are presented. The hoopoe dataset is tailored to DES Y1 and includes realistic blending, spatial masks and variation in the point spread function. We derive shear corrections, which we show are robust to changes in calibration method, galaxy binning and variance within the simulated dataset. Sources of systematic uncertainty in the simulation-based shear calibration are discussed, leading to a final estimate of the 1 sigma uncertainties in the residual multiplicative bias after calibration of 0.025. Chapter 4 describes an extension of the analysis on the hoopoe simulations into a detailed investigation of the impact of galaxy neighbours on shape measurement and shear cosmology. Four mechanisms by which neighbours can have a non-negligible influence on shear measurement are identified. These effects, if ignored, would contribute a net multiplicative bias of m ~ 0.03 - 0.09 in DES Y1, though the precise impact will depend on both the measurement code and the selection cuts applied. We use the cosmological inference pipeline of DES Y1 to explore the cosmological implications of neighbour bias and show that omitting blending from the calibration simulation for DES Y1 would bias the inferred clustering amplitude S8 = sigma_8 (Omega_m /0.3)^0.5 by 1.5 sigma towards low values. Finally, we use the hoopoe simulations to test the effect of neighbour-induced spatial correlations in the multiplicative bias. We find the cosmological impact to be subdominant to statistical error at the current level of precision. Another major uncertainty in shear cosmology is the accuracy of our ensemble redshift distributions. Chapter 5 presents a numerical investigation into the combined constraining power of cosmic shear, galaxy clustering and their cross-correlation in DES Y1, and the potential for internal calibration of redshift errors. Introducing a moderate uniform bias into the redshift distributions used to model the weak lensing (WL) galaxies is shown to produce a > 2 sigma bias in S8. We demonstrate that this cosmological bias can be eliminated by marginalising over redshift error nuisance parameters. Strikingly, the cosmological constraint of the combined dataset is largely undiminished by the loss of prior information on the WL distributions. We demonstrate that this implicit self-calibration is the result of complementary degeneracy directions in the combined data. In Chapter 6 we present the preliminary results of an investigation into galaxy intrinsic alignments. Using the DES Y1 data, we show a clear dependence in alignment amplitude on galaxy type, in agreement with previous results. We subject these findings to a series of initial robustness tests. We conclude with a short overview of the work presented, and discuss prospects for the future.

Weak gravitational lensing has developed to be one of the most powerful tools for studying the (dark) matter distribution in the Universe. Most weak lensing studies thus far were con- ducted in the optical and near infrared. Measuring weak lensing in the radio though, provided it is feasible, can be very advantageous. One can exploit the well known and deterministic beam pattern of a radio telescope and the polarisation information in radio data to reduce shape biases and intrinsic alignment effects respectively. Combining the information from an optical and a radio survey can also help remove systematics from both datasets. This has motivated this study that uses archival radio and optical data to treat telescope systematics and measure an unbiased weak lensing signal using shape information derived from radio observations. Using simulations I have shown that an unbiased convergence cross power spectrum can be measured in the presence of the large scale (θ > 1◦) systematics detected in FIRST and SDSS. The method however amplifies the uncertainties by a factor ∼2.5 compared to the errors due to cosmic variance and noise due to galaxy intrinsic shape alone. Using the shape information from the two surveys I measure a Ckappakappa spectrum signal that is inconsistent with zero at the 2.7sigma. The placed constraints are consistent with the expected signal in the concordance cosmological model assuming recent estimates of the cosmological parameters from the Planck satellite and literature values for the median redshifts of SDSS and FIRST.Through simulations I also show that I can successfully remove position based small scale systematics (θ5). Using the deconvolved information for the resolved sources I calculate a FWHM median size and flux density of 0.5'' and 300μJy respectively. Comparing the source number density and RMS noise of the study with those of FIRST, I extrapolate to predict that the number density of sources at > 5sigma will be ∼5arcmin-2, assuming the target noise threshold for the survey is reached.