Bachelor Thesis With Prof. Lesgourgues in 2021

 

1. Measuring cosmological distances with gravitational waves

Knowing the distance to very remote objects is always a challenge in cosmology. This is however the key to understand in which way our universe expands, and what it is made of. Traditional techniques are based on objects called ``standard candles'' (supernovae) and ``standard rulers''. A new technique is emerging thanks to the observation of gravitational waves: ``standard sirens''. The student will read some basic literature about the expanding universe (the Friedmann model) and about gravitational waves (in analogy to electromagnetic waves). Then they will try to understand the overall principle of the ``standard siren'' technique, and to summarise the main equations. Finally they will implement these equations in a small numerical module (of O(50) lines only) within the software package developed by the RWTH cosmology group, in order to forecast the sensitivity of future experiments to this technique.

Skills required: mainly, ability to quickly understand articles and reproduce calculations, also some minimal coding skills (python preferred)

Main supervisor: Prof. Julien Lesgourgues

2. Efficient integration of sources using an expansion on separable templates

Present day cosmology mostly exploits the observed two-point correlations of various probes such as the cosmic microwave background or galaxy number counts. With the more precise future experiments the information can be more optimally utilised by including also higher point statistics. This however poses new computational challenges as realistic models often involve numerically costly integrations over non-separable source functions. To avoid this challenge simplified models are often studied in which only a few separable shapes appear, which can be integrated and analysed in an efficient way. We have developed the Einstein-Boltzmann code SONG that outputs realistic non-separable sources as an interpolation table. The Bachelor student will use this data and attempt to identify a set of separable basis-functions that is able to approximate the numerical solution to high precision. The goal is to write a small code in C that reads an interpolation table and outputs the optimal coefficients for expansion on the chosen set of basis functions. This functionality will then enable an efficient analysis in the well established framework of separable basis functions.

Skills required: numerics, programming (in C)

Main supervisor: Dr. Christian Fidler

3. Retraining Neural Networks to predict the results of universe simulations

The RWTH cosmology group develops numerical simulation tools to predict the properties of the universe on large scales as a function of cosmological parameters which describe the content of the universe. Recently, we have been able to train neural networks in order to predict the simulation results in a significantly (but not considerably) shorter amount of time. The student will contribute to this effort by retraining the networks with different hyperparameter values in order to search for a higher accuracy-over-evaluation-time ratio.

Skills required: prior knowledge on neural networks, fluency in python, passion for numerics

Main supervisor: Prof. Julien Lesgourgues together with his students