Cosmological sphaleron from real tunneling and its fate.

We show that the cosmological sphaleron of the Einstein-Yang-Mills system can be produced from real tunneling geometries. The sphaleron will tend to roll down to the vacuum or pure gauge field configuration, when the universe evolves in the Lorentzian signature region with the sphaleron and the corresponding hypersurface being the initial data for the Yang-Mills field and the universe, respectively. However, we can also show that the sphaleron, although unstable, can be regarded as a pseudostable solution because its lifetime is even much greater than that of the universe. PACS number(s): 98.80.Hw, 98.80.Cq. ∗Electronic address: [email protected]