Cosmic shear analysis from theory to data
One of the most important challenges in cosmology today is understanding the dark matter and dark energy which composite together 95% of the cosmic energy density of the Universe. Weak gravitational lensing by large scale structures is one of the most promising probes for understanding these components and therefore the Universe. The imaging surveys of the future will cover wider fields of view, more accurate redshift estimations and deeper galaxy images. This will leads to smaller statistical errors and tighter parameter constraints. This increased statistical precision will not be satisfactory, however, unless there are trustworthy and accurate methods to analyse the data in order to extract all the information they can offer. In this thesis I will explore two cosmic shear analysis methods, COSEBIs (Complete Orthogonal Sets of E-/B-Integrals) and PCls (Pseudo Cls). Both of these methods are able to separate gravitational lensing effects (E-modes) from the contaminants (B-modes). A prominent challenge for cosmological surveys is the estimation of accurate data covariances. N-body cosmological simulations are the most common method used for estimating the covariance, but a large number of simulations with high enough resolution have to be run to estimate accurate data covariances. This number grows with the number of data points used in the analysis. Running cosmological simulations is time consuming and expensive. Therefore, data compression is highly desirable for many disciplines. In Chapter 3 I introduce a method that optimally compresses the number of observables according to their sensitivity to the parameters to be estimated. I then apply this method to COSEBIs (Complete Orthogonal Sets of E-/B-Integrals), an analysis method for weak gravitational lensing, and show that the compressed observables are not sensitive to the choice of the input covariance matrix used to define them. In Chapter 4 I set up a blind analysis of CFHTLenS2 , the state-of-the-art weak gravitational lensing survey, using COSEBIs and their compressed version. I present a likelihood analysis to estimate cosmological parameters from the data. This is the first time this form of optimised compression has been applied to data. I will also use tomographic redshift bins with COSEBIs and compressed COSEBIs for the first time. The tightest constraints I find for the best cosmological parameter combination is σ8(Ωm/0.27)0.62 = 0.825+0.033−0.044, which is consistent with previous analysis of CFHTLenS data. In Chapter 5 I employ Gaussian and lognormal simulated shear fields to explore a flat sky Pseudo Cl analysis pipeline which I have developed. Although, shear two-point correlation functions are insensitive to the mask which are always present on galaxy images, their Fourier counterparts, shear power spectra, are biased by them. Therefore, the effects of masking should be considered in Fourier space analysis of weak gravitational lensing data. I use different masks and propagate errors to cosmological parameters using Fisher analysis to explore the limitations and strengths of Pseudo Cl method. In the final Chapter I will conclude that the studies presented in this thesis strongly advocates and prefers the use of the presented methods in Chapters 3 and 4, for any future analysis of weak gravitational lensing data. In addition, the compression method in Chapter 3 can also be applied to other cosmological analysis. And finally to avoid biased results Pseudo Cl analysis for the future surveys have to be performed with the considerations detailed in Chapter 5.