This thesis is concerned with developing new methods for performing weak gravitational lensing with the aim of addressing specific systematic effects in weak lensing surveys. The first of these effects is the multiplicative biases which arise as a result of isotropic smearing. This smearing may be due to atmospheric seeing or an instrumental PSF. Isotropic smearing circularizes a galaxy image and leads to a systematic under-estimate of the modulus of the observed ellipticity. The orientation of the observed galaxy is, however, unaffected. We exploit this property by formulating a weak lensing shear estimator that requires measurements of galaxy position angles only, thereby avoiding the contribution from this systematic. We demonstrate the method on simulations and the CFHTLenS data by reconstructing convergence maps and comparing the results with the standard full ellipticity based approach. We show that the difference between the reconstructed maps for the two approaches is consistent with noise in all of the tests performed. We then apply the technique to the GREAT3 challenge data using three distinct methods to measure the position angles of the galaxies. For all three methods, we find that the position angle-only approach yields shear estimates with a performance comparable with current well established shape based techniques. The second effect addressed arises from the intrinsic alignment of the source galaxies. This alignment mimics a shear signal, and hence biases estimates of the shear. To mitigate this effect, we develop three shear estimators that include polarization information from radio observations as a tracer of a galaxy’s intrinsic orientation. In addition to the shear estimator, we also develop estimators for the intrinsic alignment signal. We test these estimators by successfully reconstructing the shear and intrinsic alignment auto and cross-power spectra across three overlapping redshift bins.

This thesis will present a new cosmic shear analysis pipeline SUNGLASS (Simulated UNiverses for Gravitational Lensing Analysis and Shear Surveys). SUNGLASS is a pipeline that rapidly generates simulated universes for weak lensing and cosmic shear analysis. The pipeline forms suites of cosmological N-body simulations and performs tomographic cosmic shear analysis using a novel line-of-sight integration through the simulations while saving the particle lightcone information. Galaxy shear and convergence catalogues with realistic 3-D galaxy redshift distributions are produced for the purposes of testing weak lensing analysis techniques and generating covariance matrices for data analysis and cosmological parameter estimation. This thesis presents a suite of fast medium-resolution simulations with shear and convergence maps for a generic 100 square degree survey out to a redshift of z = 1.5, with angular power spectra agreeing with the theoretical expectations to better than a few percent accuracy up to ℓ = 103 for all source redshifts up to z = 1.5 and wavenumbers up to ℓ = 2000 for source redshifts z ≥ 1.1. A two-parameter Gaussian likelihood analysis of Ωm and σ8 is also performed on the suite of simulations for a 2-D weak lensing survey, demonstrating that the cosmological parameters are recovered from the simulations and the covariance matrices are stable for data analysis, with negligible bias. An investigation into the accuracy of traditional Fisher matrix calculations is presented. Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment, and to optimise the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimisation it is usually assumed the power-spectra covariance matrix is diagonal in Fourier-space. But in the low-redshift Universe, non-linear mode-coupling will tend to correlate small-scale power, moving information from lower to higher-order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this thesis, the loss of information is quantified by comparing näıve Gaussian Fisher matrix forecasts with a Maximum Likelihood parameter estimation analysis of the suite of mock weak lensing catalogues derived from the SUNGLASS pipeline, for 2-D and tomographic shear analyses of a Euclid-like survey. In both cases the 68% confidence area of the Ωm − σ8 plane is found to increase by a factor 5. However, the marginal errors increase by just 20 to 40%. A new method is proposed to model the effects of non-linear shear-power mode-coupling in the Fisher Matrix by approximating the shear-power distribution as a multivariate Gaussian with a covariance matrix derived from the mock weak lensing survey. The findings in this thesis show that this approximation can reproduce the 68% confidence regions of the full Maximum Likelihood analysis in the Ωm − σ8 plane to high accuracy for both 2-D and tomographic weak lensing surveys. Finally, three multi-parameter analyses of (Ωm, σ8, ns), (Ωm, σ8, ns, ΩΛ)and (Ωm, σ8, h, ns, w0, wa) are performed to compare the Gaussian and non-linear mode-coupled Fisher matrix contours. The multi-parameter volumes of the 1σ error contours for the six-parameter non-linear Fisher analysis are consistently larger than for the Gaussian case, and the shape of the 68% confidence volume is modified. These results strongly suggest that future Fisher Matrix estimates of cosmological parameter accuracies should include mode-coupling effects.