The cosmic large scale structure: non-linear dynamics and non-Gaussian statistics

Themes: mathematical sciences and physical sciences
Research areas: mathematical physics, non-linear systems
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Cosmology, the study of the universe on the largest length and time scales, has been at the heart of human questions for millenia. Understanding our place in, the origins of, and the ultimate fate of the universe are some of the most fundamental questions asked. In the last century, we have begun to answer these questions not simply with philosophical speculation, but through empirical and scientific enquiry. This scientific approach to cosmology began in earnest in the 1920s when measurements of distant galaxies indicated that the universe was not static, and was in fact expanding. In 1998, measurements of distant dying stars indicated that the universe is not only expanding, but accelerating. The last decade, and the promise of large scale near future experiments puts us firmly into the era of precision cosmology, where we can make statements about the contents and dynamics of the universe with associated errors at or below the percent level.

Predictions in cosmology are by nature statistical. For example, we cannot predict if there will be a galaxy at any given position in the sky, which would require exact knowledge of the initial conditions of the universe, but we can make statements about the statistics of observable quantities such as galaxy positions. To date, most of the strong constraints in cosmology come from measuring the statistics of the cosmic microwave background (CMB), light from 370,000 years after the big bang. While this has provided a strong starting place for modern cosmology, the large scale structure of the universe - a weblike network of dark matter and galaxies - potentially holds orders of magnitude more information than the CMB. Accessing information about cosmology and fundamental physics from this cosmic structure is the focus of my project.

My research focuses on two particular aspects of large scale structure. The first of my project is better understanding the nonlinear gravitational dynamics of dark matter. As the dark matter outnumbers "normal" matter 4 to 1, it is the driving force in the formation of large structures. However, standard treatments of dark matter dynamics are only valid above a certain length scale, below which the equations of motion become nonlinear. Understanding this nonlinear regime is crucial for understanding bound structures called dark matter halos, which host galaxies and set the skeleton of the large scale structure. My project will focus on novel techniques to describe gravitational dark matter dynamics, in particular using the quantum-classical correspondence and its links to quantum fluid phenomena (including vorticity and turbulence). The goal is to develop new analytical and computational tools to solve the time-evolution of dark matter into this nonlinear regime and to hunt for the characteristic signature of particular dark matter candidates.

The second aspect is developing novel statistical techniques that can be used to extract constraints on current cosmological parameters and investigate new fundamental physics. These techniques are based on choosing statistics with particular symmetries, for which powerful mathematical principles (from large deviation theory) ensure that the dominant contribution to the dynamics also has this same symmetry. Using a few physical ingredients we can predict these statistics from first principles - including their dependence on fundamental parameters describing gravity, neutrino masses, or the early universe. These techniques can extract additional information from the non-Gaussian statistics of the matter distribution that are lost in standard cosmological analysis techniques, providing powerful and complementary routes of investigation.