250155 VU Cosmic Structures: Theory, Numerics and Statistics (2022W)

The formation of complex structure in our Universe from quantum fluctuations is one of the key topics of modern cosmology. The goal of this course is to study the wide range of theoretical techniques (analytical, numerical, statistical) used in the context of cosmic structure formation. The course will provide a concise introduction to cosmology with a focus on the large-scale structure (i.e. the inhomogeneous distribution of matter on large scales). We will motivate the key equations and then approach their solutions and the associated phenomenology using various techniques. This course is aimed at a broad audience of students in applied mathematics, physics, astrophysics, or computational science. We will touch on a wide range of topics in applied mathematics such as (not in chronological order)
- random fields, excursion sets
- spatial statistics: correlation functions, power spectrum
- analytical methods for PDEs and ODEs, perturbation theory and asymptotic methods
- numerical solutions of PDEs and ODEs,
- numerical N-body methods, and
- data analysis
Also the relevant (astro-)physical concepts in cosmology (inflation, cosmic microwave background, Newtonian gravity in an expanding universe, the Vlasov-Poisson system, …) will be introduced and discussed.

An important aspect of the course will be hands-on exercises based on (1) numerical experiments with Python, as well as (2) analytical/perturbative calculations.

Some familiarity with Python is helpful. Please note that familiarity with General Relativity/Differential Geometry or Astrophysics is not a pre-requisite for this course.