On the effect of projections on convergence peak counts and Minkowski functionals

The act of projecting data sampled on the surface of the celestial sphere onto a regular grid on the plane can introduce error and a loss of information. This paper evaluates the effects of different planar projections on non-Gaussian statistics of weak lensing convergence maps. In particular we investigate the effect of projection on peak counts and Minkowski Functionals (MFs) derived from convergence maps and the suitability of a number of projections at matching the peak counts and MFs obtained from a sphere. We find that the peak counts derived from planar projections consistently overestimate the counts at low SNR thresholds and underestimate at high SNR thresholds across the projections evaluated, although the difference is reduced when smoothing of the maps is increased. In the case of the Minkowski Functionals, V0 is minimally affected by projection used, while projected V1 and V2 are consistently overestimated with respect to the spherical case

Weak Lensing Techniques on the Curved Sky

Future weak lensing surveys will cover larger areas of the sky that necessitate analysis on the curved sky geometry instead of projections to the plane. This thesis focuses on reconstructing convergence maps from cosmic shear on the curved sky geometry. These convergence maps are useful tools for cosmological analysis, including probing non-Gaussian properties. The first chapter focuses on evaluating the performance of different methods of projecting simulated shear data from the curved sky to the plane, to subsequently undergo Kaiser-Squires reconstruction and analysis, and drawing comparisons to reconstruction and analysis directly on the sphere, using peak counts and Minkowski Functionals as the statistics selected for comparison. It is found that projections to the plane are only effective for small areas and it is preferable to perform analysis directly on the sphere when possible. Under ideal circumstances, peak counts derived from data projected using the sine and orthographic projections are most accurate to the spherical case. For the Minkowski Functionals there are significant differences that persist even when attempting to mitigate the projection effects. While certain projections allow reasonable approximations of the spherical sky geometry, it is impractical to use such projections on data covering large areas of the sky and performing analysis on the spherical setting is preferable. The second and third chapters focus on the separation of E-modes and B-modes through wavelet pure mode estimators on the sphere, which cancel mode mixing caused by masking of the shear data. The aim is to remove ambiguous modes to produce pure E-B modes, providing greater accuracy for studying cosmology from them. An evaluation of the accuracy of this method is performed using simulated data to compare the Kaiser-Squires, harmonic pure estimator and wavelet pure estimator methods. This finds a significant improvement in the accuracy of recovering simulated E-modes and B-modes when using the wavelet pure estimator, over the Kaiser-Squires method and harmonic pure estimator. This wavelet pure estimator method is applied to DES Y1 data and statistics, including the Minkowski Functionals, are derived and discussed. The wavelet pure estimator successfully reconstructs the E-mode and B-mode maps accurate to previous studies of the data. The Minkowski Functionals of the E-modes and B-modes display distinct differences to the analytic form for a 2D Gaussian random field. A new problem is discovered in the apodisation of the data near the mask boundary, and a potential solution is attempted through identifying and removing apodised pixels with a new mask