There are many open questions in cosmology, chief among which are the nature of the dominant components in the Universe: dark energy and dark matter. One promising probe with which to make progress in answering these questions is the analysis of weak gravitational lensing: subtle distortions in the shapes of distant galaxies due to the gravitational effect of largescale structure in the Universe. These distortions depend closely on the properties of dark energy and dark matter, which govern the evolution of structure in recent times. Careful statistical analysis of the distortions may therefore place tight constraints on physical theories of these components, along with gravity and other constituents of the Universe such as neutrinos. This promise is set to be realised by the upcoming generation of weak lensing experiments such as the Euclid space mission and the Square Kilometre Array radio observatory, which will observe tens of billions of galaxies, and in doing so will achieve an unprecedented level of statistical precision on cosmological constraints. However, such unprecedented precision requires equally unprecedented understanding and control of all aspects of the analysis process, in order to obtain reliable results and avoid undiagnosed biases and systematic errors. This thesis makes progress towards a complete and robust understanding of certain aspects of weak lensing analyses. Chapters 36 focus on pseudoCl estimators, which are fast estimators of twopoint correlation in Fourier space, for use with partialsky observations. The exact joint likelihood of pseudoCl estimates from an arbitrary number of correlated spin0 and spin2 Gaussian fields is derived and validated in Chapter 3. It is shown in Chapter 4 that to obtain accurate constraints on dark energy parameters with pseudoCl estimates from Euclid, a Gaussian likelihood is sufficiently accurate, and that this accuracy is robust to the details of the analysis setup. A Gaussian likelihood requires a covariance matrix, and in Chapter 5 a method is presented with which to calculate a complete covariance matrix of pseudoCl estimates for Euclid, including nonGaussian mode coupling arising from nonlinear structure growth as well as Gaussian mode coupling arising from the convolution of the signal with the mask describing the details of the sky coverage. The resulting covariance matrix is compared to one estimated from weak lensing simulations, with good agreement. Chapter 6 turns to the question of how to select an angular binning strategy to strike an optimal balance between statistical constraining power and data compression. Finally, Chapter 7 considers a different question, of whether convolutional neural networks may be used to estimate weak lensing shear directly from radio visibilities from the Square Kilometre Array. Working towards this aim from a simplified case of lensing of the cosmic microwave background, it shows that this method is promising but also entails many challenges. The work presented in this thesis helps to make significant progress towards an ultimate goal of reliable cosmological inference from future weak lensing data, but many challenges and open questions remain, which are discussed in Chapter 8.
Date of Award  31 Dec 2022 

Original language  English 

Awarding Institution   The University of Manchester


Supervisor  Lee Whittaker (Supervisor) & Michael Brown (Supervisor) 

 analysis methods
 weak gravitational lensing
 cosmology
Analysis methods for precision cosmology with weak gravitational lensing
Upham, R. (Author). 31 Dec 2022
Student thesis: Phd