YANG-MILLS COSMOLOGIES AND COLLAPSING GRAVITATIONAL SPHALERONS

Cosmological solutions with a homogeneous Yang-Mills field which oscil lates and passes between topologically distinct vacua are discussed. T hese solutions are used to model the collapsing Bartnik-McKinnon gravi tational sphaleron and the associated anomalous production of fermions . The Dirac equation is analyzed in these backgrounds. It is shown exp licitly that a fermion energy level crosses from the negative to posit ive energy spectrum as the gauge field evolves between the topological ly distinct vacua. The cosmological solutions are also generalized to include an axion field.