Towards a UV-complete Standard Model: From baryogenesis to asymptotic safety

In this dissertation we investigate aspects of the UV completion of the Standard Model of particle physics. We focus on two examples that inevitably require new degrees of freedom: baryon asymmetry and quantum gravity. Baryogenesis can occur at the electroweak phase transition if new physics triggers the phase transition to be of strong first order. We consider generic classes of beyond the Standard Model physics and show that all of them give rise to a strongly enhanced Higgs self-coupling if we demand electroweak baryogenesis. The Higgs self-coupling will be measured precisely enough in the high-luminosity run of the LHC. Quantum gravity is investigated with the asymptotic safety approach, which conjectures the existence of a UV fixed point of the renormalisation group flow. The latter allows for a non-perturbative renormalisation of quantum gravity. We develop the approach towards quantitative precision by systematically computing flows of higher-order correlation functions. We start from a minimal setup that includes a genuine Newton's coupling, which is the setup with the graviton two- and three-point function. In a first extension we include the graviton four-point function, which allows to investigate convergence properties and the restoration of diffeomorphism symmetry in the IR. In a second extension we evaluate the correlation functions on a constantly-curved background. From this we set up the equations of motion and find a solution at negative background curvature. Overall, these results add further significant evidence for the existence of the UV fixed point. We include Standard Model matter content into the quantum gravity setup. We start with minimally coupled scalars and fermions and subsequently also couple Yang-Mills theory to quantum gravity. We provide a formal argument that such systems must be compatible with asymptotic safety independent of the number of gauge or matter fields. Furthermore we show an effective universality between different avatars of Newton's coupling, which means that their flows are in quantitative agreement in the scaling region of the UV fixed point. These results are the basis for future investigations of the Standard Model fully coupled to quantum gravity