title: Exploring the dark sector with higher-order statistics
Creators: name: Grewal, Nisha
Publisher: name: The University of Edinburgh
Year: 2025
Subjects: subject: dark matter
subject: dark energy
subject: dark sector
subject: gravitational lensing
subject: two-point statistics
subject: Minkowski functionals
subject: Legacy Survey of Space and Time
subject: LSST
subject: machine learning
subject: cosmic shear

description: To better understand the history of the dark matter distribution, we use maps of the Universe to constrain cosmological parameters that describe the characteristics of dark matter and dark energy. Various statistics calculated from cosmological models have been used to measure and constrain parameters that characterise different structures and effects in the Universe. Statistics measured from gravitational lensing have been highly effective in probing the growth of large-scale structures, as well as the accelerating expansion of the Universe. Statistics measured from clustering and convergence maps can measure such mass characteristics, which are then compared to theory predictions. Two-point statistics are a powerful tool for constraining cosmology, with systematics and measurement errors well understood. However, they can only measure signal from Gaussian fields, where the collection of points have a Gaussian distribution. Even though they do not capture non-Gaussian information on small-scale structures, statistics involving two points have still been able to achieve precise constraints when measured from weak lensing maps. To capture non-Gaussian information on small-scales, I go beyond two-point and measure higher-order statistics in search of stronger constraints on cosmological parameters. In my first chapter, I investigate the inclusion of clustering maps in a weak lensing Minkowski Functional (MF) analysis of Stage III and Stage IV survey simulations to constrain cosmological parameters. The standard 3x2pt approach to convergence and clustering data uses two-point correlations as its primary statistic; MFs, morphological statistics describing the shape of matter fields, provide additional information for non-Gaussian fields. Previous analyses have studied MFs of lensing convergence maps; in this chapter I explore their simultaneous application to clustering maps. I employ a simplified linear galaxy bias model, and using a lognormal curved sky measurement and Monte Carlo Markov Chain (MCMC) sampling process for parameter inference, I find that MFs do not capture any additional signal compared to a 3x2pt analysis. However, I argue that MFs should improve constraining power when nonlinear baryonic and other small-scale effects are taken into account. As with a 3x2pt analysis, I find a significant improvement to constraints when adding clustering data to MF-only and MF+3x2pt weak lensing measurements, and strongly recommend future higher order statistics be measured from both convergence and clustering maps. The process of converting cosmic shear maps to convergence maps involves tedious calculations. Various mass mapping reconstruction methods have been developed to simplify the process. In the second chapter, I evaluate the retention of signal information of four reconstruction methods by measuring MFs from the output maps. Kaiser-Squires (KS) takes the maximum likelihood estimate (MLE) of the convergence map, applying Gaussian smoothing to reduce the noise. Wiener Filter is a linear filter of signal and noise that applies a maximum a posteriori (MAP) solution. Unlike KS, it can transform masked data, but neither are able to capture non-Gaussian signal very well. DarkMappy approximates the uncertainty that comes from reconstruction by reconstructing MAP convergence maps. DeepMass is a deep learning model that specialises in denoising the signal. It estimates the mean of the posterior distribution, where the iterative layered network minimises the mean squared error (MSE) between the signal and the estimate. In Chapter 3 I aim to determine which method best reconstructs the original convergence signal with efficiency and accuracy. LSST data will be even wider and deeper than any previous survey, providing even more cosmological information with higher resolution weak lensing maps. In Chapter 4, I explore the potential of higher-order statistics to extract non-Gaussian information that is not accessible through traditional two-point statistics. Specifically, I optimise the following higher-order statistics (HoS) for an LSST framework: Minkowski functionals and peak counts, which decompose the field at different scales. Measuring observables from noisy and masked LSSTlike CosmoGridV1 simulations, I compare the information captured by the two-point and higher-order statistics. Using a Fisher analysis to build contours, I assess the different statistics by forecasting their constraints on cosmological and baryonic parameters, also studying the effects of survey geometry. I find both HoS outperform two-point statistics, with MFs significantly improving precision. I highly recommend the inclusion of Minkowski functionals in future higher-order statistics analyses.