Baryogenesis and Polyakov line condensate during inflation
  The thermal average of the Polyakov line is non-zero at high temperature. It has been suggested that its phase could be relevant for baryogenesis within the standard model, providing a source of spontaneously broken CP violation. This scenario suffers from a causal domain problem which cannot be cured by inflation: quantum fluctuations in de Sitter space overwhelm the periodicity of the potential. 
As. Abada, M.B. Gavela and O. P\`ene