# Table of contents

- 1.1 Overview of Part I: Background Cosmology
- 1.2 Overview of Part II: Recombination History
- 1.3 Overview of Part III: Evolution of structure in the Universe
- 1.4 Overview of Part IV: The CMB and matter power-spectra

# Overview of the course

The aim of this course is to understand how the large scale structures - of both normal matter, dark matter, neutrinos and radiation - form and evolve in our Universe key and to numerically compute some key statistical observables in cosmology like the cosmic microwave background (CMB) angular power-spectrum and the matter power-spectrum. We focus on both learning how to do the theoretical calculations, implementing and solving the resulting equations numericaly and then understanding the results based on the physics that is going on. You will write up the results from your numerical project in a report written as a proper research article so you get experience with that. The course is split up in four milestones, each of which has a numerical project that you will hand in and which counts for 30% of the grade in the course. The exam will this year be an oral exam (since we cannot have normal written exams) where you will get examinated on the theory and physical understanding of the things that we go through in the lectures.

Below you can find the slides (PDF; Keynote) for the first lecture in Spring 2021 if you want a more detailed overview:

# Milestone I: Background Cosmology

## Theory:

- Crash course in General Relativity
- Introduction to theoretical cosmology
- Background cosmology and the Friedmann equations

In this first part we will give you the basic operational knowledge of working with General Relativity in cosmology. We will go through the basics of background cosmology: redshifts, distances, times, density parameters and derive the Friedmann equations from scratch.

## Numerical project:

In the numerical project we will implement the Friedmann equations and compute the conformal time and the age of the Universe. This is a minor task and is just to get you familiar with the code and how to solve differential equation.

# Milestone II: Recombination History

## Theory:

In this part we will look at the early Universe where matter and radiation forms a hot plasma. We will go through the thermal history of the Universe leading up to the key event for us which is when electrons and protons formed atoms and the cosmic microwave background was released. We will review some basic equilibrium thermodynamics and introduce the Boltzmann formalism (distribution functions and the Boltzmann equation) allowing us to go beyond equilibrium and deal with all the different matter species and the interactions between them as dictated by quantum field theory.

## Numerical project:

In the numerical project we will solve the Boltzmann equation for electrons which will give us the number density of free electrons and atoms as function of time. This will tell us when the CMB was released and the quantities we compute (optical depth for Thompson scattering) will play an important role in the next milestones.

# Milestone III: Evolution of structure in the Universe

## Theory:

In this part we finally go beyond the smooth Friedmann Universe and introduce perturbations to both the metric and the matter species. We will compute the evolution equations - the Einstein-Boltzmann equations - for all species (baryons, dark matter, photons, massless neutrinos) and the metric (gravitational potentials). We will also give a brief introduction to inflation and its key predictions which is what will give us the initial conditions for our equations.

## Numerical project:

In the numerical project we will solve this system of $\sim 20$ coupled differential equations describing perturbation of baryon and dark matter density and velocity, photon temperature perturbations and metric perturbations from the early Universe till today.

# Milestone IV: The CMB and matter power-spectra

## Theory:

In this part we will go through how to connect the perturbations we have computed to the key statistical observables: the CMB power-spectrum and the matter power-spectrum. We will go through a key technique, line of sight integration, for computing and also understanding the CMB spectrum and we will try to understand the features in the spectra and how they change with varying cosmological parameters.

## Numerical project:

In the numerical project we will go put all the pieces together from the previous milestones and compute the theoretical predictions for the CMB angular power-spectrum and the matter power-spectrum and compare these with real observations.