# Bachelor Thesis With Prof. Lesgourgues in 2020

1. Precise Initial Conditions for cosmological simulations (analytical)

Linear cosmological perturbation theory can be used to model the early Universe and the Cosmic Microwave Background (CMB) radiation. However, in the late universe, dark matter over-densities continuously grow and eventually become so large that perturbative approaches fail. Thus, to describe the formation of galaxies, we need a fully non-linear method. N-body simulations describe the process of non-linear structure formation, starting from tiny initial density fluctuations and arriving to the formation of the structures (galaxies, clusters) that we observe today. They simulate the gravitational forces between a large number of individual particles that represent the dark matter distribution in the Universe.

The initial conditions for these simulations are usually set in the early Universe, when the fluctuations are still small and can be described using cosmological perturbation theory. Since the precision of the entire simulation cannot exceed that of the initial conditions, various analytical methods are employed to model the early Universe as precisely as possible.

The task of the student is to learn these state-of-the-art analytical models, including Eulerian and Lagrangian perturbation theory. Currently, most simulations employ second-order Lagrangian Perturbation Theory (2LPT) to generate the initial matter distribution. The goal of this project is to research extensions of this model, including decaying modes and leading third order corrections.

**Skills required:** analytical skills

**Skills learned:** some aspects of classical field theory and hydrodynamics

**Main supervisor:** Dr. Christian Fidler (together with Prof. Julien Lesgourgues)

2. Machine learning for the initialisation of cosmological simulations

While topic 1 is focused on analytic research, this project explores modern machine learning techniques. The goal is to be able to generate quickly some initial random snapshots of the distribution of Dark Matter in the early universe that are compatible with a given theoretical 2-point correlation function. Such snapshots are used as initial conditions by the cosmological N-body simulations described in topic 1.

Generative Adversarial Networks (GANs) are a relatively recent development in machine learning, where two neural networks are trained in an adversarial setup. The first network (the generator) outputs a generated image, while the second network (the discriminator) tries to decide if this picture is real or fake. The generator never sees the training data and only indirectly learns by trying to fool the discriminator. In this way a network is constructed that can output an unlimited set of new pictures that are consistent with the set of training data. GANs are used in many application and can for example create realistic looking pictures of people that do not exist (www.thispersondoesnotexist.com).

The goal of the project is to explore in which way GANs can be used to generate realistic initial conditions. This method may be promising especially in cases where generating the initial condition is relatively expensive (that is, for so-called glass initial conditions or the realisation of higher-order statistical correlations). The task of the student is to learn how GANs work and then build, train and evaluate a simple network.

**Skills required:** basic programming skills (Python preferred)

**Skills learned:** some aspects of machine learning involving neural networks

**Main supervisor:** Dr. Christian Fidler

3. Euclid satellite and calculation of the angular power spectrum

The Euclid satellite mission (launch 2022) will map the galaxies in our universe to unprecedented precision. This will allow cosmologists to put tight constraints on the parameters of the standard model of cosmology, and shed light on the nature of dark energy, modified gravity, dark matter, and inflation. The student will investigate aspects of the calculation of the angular power spectrum of galaxy counts and galaxy weak lensing, which can be used to compare the theory and observations of galaxy clustering.

The student will mainly work on two approaches for speeding up this calculation, to make cosmological parameter extraction more feasible. Thus, this project is strongly related to mathematical and analytical methods for performing efficient multi-dimensional integrals of oscillatory functions, expanding quantities in different bases of orthogonal functions, etc.

**Skills required:** Basic mathematical and programming skills (Python or C++)

**Skills learned:** Cosmology of galaxy clustering and weak lensing, Numerical methods

(Interpolation, Integration)

**Main supervisor:** M. Sc. Nils Schöneberg (together with Prof. Julien Lesgourgues)

4. How to model the reionization of the universe analytically

A few billion years ago, the universe got ionized. Before that, it was filled with an approximately neutral gas of hydrogen and helium. After the appearance of the first stars, some bubbles of ionized gas formed, expanded, and merged to gradually ionize the gas in the whole universe.

Several more or less realistic and refined analytical models of reionisation have been described in the literature. The goal of this project is to study a few published articles on this topic, understand them at a basic level, identify the most important equations and compare models and notations. This work will be very useful for the cosmology group, since it will be a first step before the writing of a numerical simulation code, once the bachelor project is finished. If the student is very fast and also interested in numerics, they could even start on this part.

**Skills required:** taste for understanding and modeling complex physical processes (involving electromagnetism, hydrodynamics, statistics...)

**Skills learned:** knowledge of one stage in the cosmological evolution, currently considered as a hot research topic

**Main supervisor:** Prof. Julien Lesgourgues (together with M. Sc. Nils Schöneberg)

5. Constraining cosmological inflation with CMB anisotropies and distorsions

The Aachen cosmology group has developed some numerical tools for computing the theoretical predictions associated to given cosmological models, and for comparing them with astrophysical data. In this project, the student will not need to significantly change or develop these tools. They will mainly to use them in order to confront new models to new data sets. The idea is to compare two categories of models (one for the stage called "comsological inflation", and one for the presence in the universe of Primordial Black Holes) to two complementary types of cosmological data sets: the map of in homogeneities in the Cosmic Microwave Background (CMB) radiation, and the frequency spectrum of the CMB. The students will consider both real data sets and mock data sets mimicking the results of future experiments. The project will allow to get new bounds on these models, and to predic how sensitive future epxeriments will be to the parameters of these models.

**Skills required:** basic numerical skills (use of linux, running codes in python and C)

**Skills learned:** broad overview of CMB physics; advanced statistical algorithms for Bayesian parameter inference from data (with Monte Carlo Markov Chains)

**Main supervisor:** Prof. Julien Lesgourgues and M. Sc. Nils Schöneberg