Numerical methods for cosmology: from early to late times
Numerical methods are a very important tool in cosmology to describe linear (at early times) and non-linear (at late times) evolution of perturbations or to constrain parameters of a given cosmological model. Einstein-Boltzmann codes are usually used to infer the temperature power spectrum of the CMB radiation, while highly complex and sophisticated N-body and hydrodynamical simulations are required to understand how the universe evolved to form structures as we observe them today.
In these lectures I will introduce the fundamentals required to understand the structure and the implementation of the different codes normally used in cosmology and which kind of physics they allow us to describe. I will discuss the state-of-the-art in the field and what has to be done next. In particular I will cover two main groups of codes: large scale structures (N-body and Semi-Analytic Models) and Einstein-Boltzmann codes, with possibly a short discussion on MCMC methods associated to them.