Cosmological Applications of Extreme Value Statistics

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Extreme-value statistics (EVS) is a tool that can be used to quantify the rarity of extreme events. It has been widely used to predict real-world extreme events, for example extreme floods, side effects of drugs, and mutational events during evolution. In cosmology and astrophysics, it is possible to use EVS to model the abundances of rare objects, such as the most massive galaxy clusters in the Universe, the largest cosmic voids, the most massive primordial black holes, and black holes with extreme spin. EVS is a timely area of research given the new generation of experiments such as the recently launched James-Webb Space Telescope (JWST) and Euclid satellite. Using EVS, we can make predictions about the nature and abundances of extreme astrophysical objects such as galaxies, black holes and clusters.This project explores the two main formulations of EVS, namely the Generalised Extreme Value (GEV) approach, and the Peaks-Over Threshold (POT) approach. Starting with data described by some underlying probability density function (pdf) or the cumulative density function (cdf), we apply one of the two EVS methodologies. Both yield different measures of rare events.Currently, the project focuses on using EVS to predict the luminosity of the brightest galaxies at redshifts 10-15 (which have been observed by JWST). We use the GEV approach to calculate the brightest magnitude of galaxies based off various luminosity functions. We then produce graphs which show the predicted peak magnitude over a range of redshifts. We can then compare our EVS predictions to real data. The overall project will contain multiple projects of these cosmological applications. Other possible topics besides the most luminous galaxies include: -Extreme-spin binary systems and their associated gravitational waves. -Extreme mass of active galactic nuclei. The project is interdisciplinary in nature and adds to the diversity of research within Warwick's Mathematics institute. The work involves an intersection of mathematics, statistics, physics, and computing. The spirit of the project is to apply mathematical techniques to model physical observations, such that it requires a good understanding of general relativity and theoretical cosmology. Extreme-value statistics and Bayesian parameter inference are key, as well as the use of Python required to perform data analysis and statistical simulations.Prof. Joseph Silk (Institut d'Astrophysique de Paris) and Dr. Teeraparb Chantavat (Institute for Fundamental Study, Thailand) are collaborators on the current project, both of whom are long-term collaborators of Siri Chongchitnan. Work will also potentially involve collaboration with other maths and astrophysics staff at Warwick.