Volume 197, number 1,2 PHYSICS LETTERS B 22 October 1987 BARYON ASYMMETRY OF THE UNIVERSE. A MONTE CARLO STUDY ON THE LATTICE J. AMBJORN The Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen 0, Denmark M. LAURSEN Nordita, Blegdamsvej 17, 2100 Copenhagen 0, Denmark and M.E. SHAPOSHNIKOV The Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen O, Denmark and Institute of Nuclear Research, Moscow 117312, USSR Received 8 July 1987 We initiate the lattice investigation of the baryon asymmetry generation within the framework of the standard electroweak theory. We find that transitions between different gauge sectors are unsuppressed at temperatures larger than the critical temper- ature corresponding to the breaking of the electroweak SU(2) XU(1 ) group. The Monte Carlo data suggestthat the high-temper- ature plasma is populated with gauge-Higgs fluctuations, which produce a change of the Chern-Simons number of + 1 during the transition, thereby creating 12 fermions due to the electroweakanomaly. If there is a Bose-Einstein condensation of these fluctua- tions our results indicate that the baryon asymmetry produced during the phase transition could be as large as 10 6 I. Introduction It is an old observation that the anomaly of the fer- mionic current in the electroweak theory leads to baryon non-conservation in this theory [ 1 ]. At zero temperature the amplitude of such processes is expo- nentially suppressed as exp(-2Zdaw), aw~l/30. However, it has now been realized that this suppres- sion presumably is absent at the high temperatures prevealing in the early universe, due to large thermal fluctuations [ 2 ]. This ensures that any baryon asym- metry, generated by GUT interactions will be washed out, unless special conditions are satisfied [ 3 ]. Further, the high rate of these baryon non-con- servation transitions at sufficiently high tempera- tures are an important ingredient of a newly proposed scenario explaining the observed baryon asymmetry in the universe (BAU) entirely within the frame- work of the standard electroweak theory [ 4,5 ]. z Permanent address. Certain aspects of the abovementioned ideas have remained hypothetical because of their non-pertur- bative nature. At temperatures higher than To the critical temperature for the first order SU (2) X U (1) symmetry restorating phase transition, the gauge bosons are massless. The theory becomes effectively three-dimensional and infrared singularities at small momentum transfer: k<g 2 accumulate to generate a non-perturbative magnetic mass term [6]. The following non-perturbative questions are important for the scenario suggested in refs. [4,5]: (a) Are transitions between different gauge sectors unsuppressed at temperatures higher than the criti- cal Tc? These transitions are responsible for an anomalous fermion-number non-conservation for T>Tc. (b) Gauge configurations might have a Chern-Simons (CS) number different from zero for T> To. To what extent does the decay of such con- figurations at T~ Tc result in the creation Of fer- mions? (c) Does the "ground state" of the gauge 0370-2693/87/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) 49