title: Maximising information from weak lensing galaxy surveys
Creators: name: Maraio, Alessandro
Publisher: name: The University of Edinburgh
Year: 2025
Subjects: subject: weak gravitational lensing
subject: large-scale statistical analyses
subject: power spectrum estimation
subject: Quadratic Maximum Likelihood estimator
subject: QML
subject: baryonic feedback
subject: hydrodynamical simulation
subject: hydro-sim

description: Weak lensing galaxy surveys are currently undergoing a dramatic revolution as the dawn of the Stage-IV surveys is upon us. The quality and quantity of data that we are to receive over the next decade dwarfs the data we have from existing observatories and will undoubtedly lead to many cosmological discoveries. Therefore, ensuring that our analysis methods are as accurate and precise as the raw data is of upmost importance, and the driving force behind this thesis and the work contained within. Understanding the details behind a modern cosmic shear analysis requires us to start with the fundamentals of cosmology and go from there. Chapter 1 provides us with a gentle introduction to some of the driving ideas and results that have compounded to form our modern cosmological model. Starting with Einstein’s general relativity, Chapter 2 derives many key results which are required for any cosmological analysis. We then focus on the specifics of a cosmic shear analysis in Chapter 3, with a brief look into some of the motivations behind the Stage-IV surveys in Chapter 4. Returning to the theme of the development of accurate and precise statistical methods for use in cosmic shear analyses, Chapter 5 investigates a new implementation of the Quadratic Maximum Likelihood (QML) estimator. Previous implementations of the QML estimator required the direct evaluation of dense, high-dimensional matrices of either spherical harmonics or Legendre polynomials. This severely limits the application of these methods to the increased precision of Stage-IV survey data. The evaluation of each entry in these matrices is a major bottleneck in computational speed, combined with the extreme limitations in the RAM usage from the high dimensionality of the matrices makes these existing implementations of QML unsuitable for the next generation of cosmic shear surveys. I led the development of a new, alternative implementation of the QML estimator which side-steps the need to compute and store these massive matrices though using the conjugate-gradient and finite-differences methods. These allow for dramatically reduced run-times and RAM usage of my new estimator when compared to previous implementations. Applying this estimator to Stage-IV cosmic shear data finds that we achieve a 20% decrement in the error bars on the largest angular scales for the E-modes, and over an order of magnitude decrement in the B-modes. This highlights the usefulness of QML methods when applied to cosmic shear survey data. An accurate measurement of the observational power spectrum is useless without robust modelling of all the systematic effects that contribute to the cosmic shear signal. Of particular importance is the impact of baryonic feedback physics that exists on small-scales within our Universe, which can dramatically affect the cosmic shear power spectrum on small angular scales. Mitigating the effects of baryonic feedback bias in cosmic shear surveys has been the discussion of many papers in the literature. Chapter 6 investigates the implementation of the ‘theoretical uncertainties’ approach applied to baryonic feedback in the matter power spectrum, the underlying quantity that cosmic shear probes. By benchmarking several baryonic feedback models to an ensemble of hydrodynamical simulations, we can quantify the error on each model as a function of wavenumber and redshift. These errors then inform us on how to smoothly down-weight the contaminating modes in the power spectrum, allowing us to gain maximum information from our observables without being susceptible to bias from inadequate modelling of baryonic feedback physics. We find that using a simple, one-parameter model of baryonic feedback leads to an unacceptable level of bias when including angular scales down to ℓ_max = 5000, the nominal target for a Stage-IV survey. The inclusion of the theoretical error covariance mitigates these biases, with the results preferring a multi-parameter model of baryonic feedback to further mitigate biases. We then turn our attention to deriving new methods for determining sets of binary scale cuts for future cosmic shear surveys in Chapter 7. Binary cuts have been well-studied in the literature, where they have been used extensively in previous Stage-III cosmic shear surveys and thus form the default choice for Stage-IV surveys. We find that if we apply existing methods for deriving binary cuts to Stage-IV survey data, then the results from our new surveys will be no better than existing results in the literature. Using this as motivation, we present three alternative methods for how the derivation of binary scale cuts might work for a Stage-IV survey. These aim to keep the maximum amount of information possible from the data, without incurring significant biases in the final results. We present a summary of work completed in this thesis along with conclusions and some thoughts for the future in Chapter 8.