Weak gravitational lensing theory and data analysis

This thesis describes methodology for analysis of weak gravitational lensing data. Weak lensing, i.e. the perturbative distortion of the images of distant objects by the gravitational deflection of light, is an important tool for understanding the distribution of matter in the universe. This is interesting because a number of extentions to the standard cosmological model, including dynamical dark energy and neutrino masses, affect the growth of structure and hence may be detectable using weak lensing. Studies of weak lensing are also motivated by lensing's ability to affect the modes in the cosmic microwave background (CMB) polarization that are sensitive to primordial gravitational waves.; Both lensing of galaxies and lensing of the CMB are considered here. The section devoted to galaxies is principally concerned with measuring the lensing-induced shape distortions from galaxy images in the Sloan Digital Sky Survey (SDSS), although the methodology will be applicable to future projects. We investigate in detail the problem of separating lensing from other shape distortions such as those induced by the atmosphere, the telescope, and photon Poisson noise. Since the intrinsic shapes of observed galaxies are not known, weak lensing observations always attempt some sort of statistical averaging over galaxies that presumably have independent orientations. We investigate the extent to which this process "averages down" the intrinsic shapes and identify a new type of bias that can affect the weak lensing power spectrum. Selection biases are considered and their importance in SDSS estimated. We present some recent cosmological results using the SDSS analysis, including new upper limits on the neutrino mass.; Lensing of the CMB has not yet been detected, nevertheless several experiments are being built that should have the sensitivity to see it. The statistical problem of extracting lensing information from the distortion of the CMB anisotropy is considered, and in the case of polarization methods are identified that allow for up to a factor of 4 reduction in noise below the standard methods. The lensing reconstruction algorithms are applied to the CMB temperature data from Wilkinson Microwave Anisotropy Probe and an upper limit is set of 3 times the expected signal.