#14 The role of the thermal function in the history of the Universe

The electroweak phase transition can be the origin of several interesting phenomena. More than being the trigger for the Higgs mechanism which gives particles mass, it can potentially explain the asymmetry between matter and antimatter in the Universe and be a source of a stochastic background of gravitational waves. In this project, we aim to compare different numerical methods for computing the thermal functions which encode the temperature dependence of the free-energy that describes this transition. These are defined from an integral without a closed-form solution which often gives imaginary results. Calculating them is a challenge, but it is essential to characterise the electroweak phase transition as strong or weak, smooth or discontinuous and to calculate the critical temperature.

Requirements: Participants should have some experience with a programming language and with a symbolic computation program like Mathematica.