Cosmological phase transitions: field theoretical and numerical improvements

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One of the biggest riddles in cosmology is the one of the observed baryon-asymmetry in the Universe: why does one observe much more baryons than anti-baryons. In principle it should be possible to explain this from the point of view of elementary particle physics via the electroweak phase transition which took place in the early Universe. However, the Standard Model fails in this respect despite the fact that it contains all required structural ingredients. Thus, it needs to be extended.In this project we will first develop fieldtheoretical and numerical methods, which allow for an improved calculation of this phase transition. It can roughly be divided into three steps: (i) the nucleation phase, in which bubbles with the energetically favourable phase nucleate, (ii) the expansion of these bubbles and (iii) collisions and coalescence of the bubbles. We will calculate the so-called bounce-solution within the 2PI-formalism, which is used to describe out-of-equilibrium phenomena. In this way we obtain a model-specific starting profile for the bubble wall and we do not rely on the usual arctan-ansatz. Moreover, one can check if one is indeed close to thermal equilibrium as it is usually assumed in the literature. This is in particular relevant for extensions of the Standard Model. In the second step we will apply these techniques to some of these extensions. We will study in particular models with an extended Higgs sector, neutral naturalness models as well as composite Higgs models taking into account the latest available LHC-data.