Measuring the dark universe with gravitational lensing

This thesis presents the use of gravitational lensing as a measure of the large-scale structure in the Universe. We detail various statistical techniques for performing and interpreting these measurements. We show evidence for the cross-correlation of cosmic microwave background (CMB) lensing with the positions of radio-loud active galactic nuclei (AGN). We demonstrate a weak- lensing cross-correlation pipeline for combining cosmic shear measurements with CMB lensing data. We forecast how cosmological parameters may be constrained through gravitational lensing measurements, with a focus on the sum of the neutrino masses, and discuss practical methods for the statistical extraction of information from data. We firstly cover the theoretical framework within which this thesis is set. We then make a comparison of sampling techniques for Bayesian parameter estimation. We find that nested sampling delivers high-fidelity estimates for posterior statistics at low computational cost, and should be adopted in favour of Metropolis-Hastings sampling in many cases. Affine-invariant MCMC is competitive when computer clusters can be utilised for massive parallelisation and, along with existing extensions to nested sampling, naturally probes multi-modal and curving distributions. Next, we correlate the positions of radio sources in the FIRST survey with CMB lensing convergence measured by the Atacama Cosmology Telescope, over 470 deg2, to determine the bias of these galaxies. We measure the angular cross-power spectrum at 4.4σ significance in the multipole range 100 < l < 3000. We fit for the overall bias-model normalisation, finding b(zeff ) = 3.5 ± 0.8 for the full sample at an effective redshift zeff = 1.5. We then present comprehensive forecasts for how the sum of the neutrino masses will be constrained with future cosmological observations. We consider prospects for the gravitationally-lensed CMB anisotropies and baryon acoustic oscillations (BAOs) in the galaxy distribution, examining how the projected uncertainty of ≈ 15 meV on the neutrino mass sum (a 4σ detection of the minimal mass) might be reached over the next decade. We find an improved optical depth measurement is important: the projected neutrino mass uncertainty increases to 26 meV if a CMB Stage 4 experiment is limited to l > 20 and combined with current large-scale polarisation data. Complementary low-redshift probes, including galaxy lensing, will play a role in distinguishing between massive neutrinos and a departure from a w = −1, flat geometry. Finally, we present a forecasting and analysis pipeline for weak-lensing cross-correlations. We introduce and motivate the joint analysis of CMB lensing and galaxy lensing, including a discussion of measurements to-date and key systematic effects in lensing data. We argue that simultaneous analysis provides a robust approach to calibration of these effects. We review the theory of weak- lensing cross-correlations, and illustrate the properties of the observables. We detail how the shear signal is extracted from the shapes of galaxies and show how this is combined with CMB lensing data to measure their cross power spectrum. We demonstrate the pipeline we have developed – from map making to parameter estimation – on real and simulated data from ACT, CFHTLenS and KiDS. We conclude by forecasting the ability of future experiments to detect the lensing cross-correlation.