Computation of the winding number diffusion rate due to the cosmological   sphaleron
  A detailed quantitative analysis of the transition process mediated by a sphaleron type non-Abelian gauge field configuration in a static Einstein universe is carried out. By examining spectra of the fluctuation operators and applying the zeta function regularization scheme, a closed analytical expression for the transition rate at the one-loop level is derived. This is a unique example of an exact solution for a sphaleron model in $3+1$ spacetime dimensions. 
Mikhail S.Volkov