Cosmological Phase Transitions and Gravitational Wave Production in Conformal Extensions of the Standard Model

Abstract

This thesis concerns the analysis of the first-order electroweak phase transition in a conformal extension of the standard model (SM). The model we consider is the classically conformal SM which is extended by a scalar doublet and a hidden SU(2) gauge group. First, we review the quantum effective action and the techniques of thermal field theory. We explain why usual perturbation theory breaks down at high temperatures and introduce a novel method to alleviate this problem by resumming diagrams with the so-called gap equation. By this approach, we restore the validity of perturbation theory at finite temperature and thus account for reliable results in the early universe. With such an improved potential at hand we study the thermal history of the universe within the context of the conformal extension of the SM and compare it with the SM results. We study the phase transitions of our model by three different approaches: Sequential symmetry breaking, Gildener-Weinberg method and the multi-field approach. In the last case, we obtain an improved effective potential dependent on two background fields which allows us to trace the global minimum in the two-dimensional field space with increasing temperature. We show that with the Gildener-Weinberg method and the multi-field approach, the conformal extension of the SM entails a strong first-order phase transition. Moreover, the multi-field approach indicates that the phase transitions in our model is a two-step transition. Using these results we analyze the process of bubble nucleation for the Gildener-Weinberg method and the multi-field approach. Finally, we estimate the stochastic gravitational wave backgrounds (SGWB) produced by the collision of bubble walls. Our estimates show that the conformal model in consideration leads to the production of a SGWB which could be detected by the prospective LISA gravitational wave detector.