Electroweak baryon number non-conservation and “topological condensates” in the early Universe

In this paper we focus on the first condition. Non-perturbative electroweak baryogenesis offers the intriguing possibility that topological features of the Standard Model might be (in part) responsible for baryon and lepton number violation in the early Universe [2, 3, 4, 5]. In this talk we argue that electroweak baryogenesis in the early Universe is accompanied by the formation of a “topological condensate” in the Standard Model vacuum [6] which (probably) survives cooling to the Universe that we observe today. The key physics involves the application of anomalous commutator theory [7, 8, 9] and renormalization group arguments to non-perturbative vacuum transition processes (sphalerons) between vacuum states characterized by different topological winding numbers. When the effect of QCD vacuum transition processes which break axial U(1) symmetry are also included the net “topological condensate” develops a spin independent component. We first outline the key features of electroweak baryogenesis and then explain the consequences of anomalous commutator theory for this physics. The existence (or otherwise) of the “topological condensate” will depend on the precise definition