It is known that baryon number inhomogeneities may arise as a consequence of electroweak baryogenesis. Their geometry, size, and amplitude depend on the parameters that characterize the baryogenesis mechanism, as well as on those that determine the phase transition dynamics. We investigate this parametric dependance. We show that in the case of the minimal supersymmetric standard model, the geometry of the inhomogeneities most probably consists of spherical regions of high density surrounded by low-density walls, in contrast to the case of the minimal standard model. In this supersymmetric extension we find that density contrasts of up to a factor of 100 may arise. This amplitude increases for higher values of the latent heat or lower values of the bubble wall tension, and can be significantly larger in different extensions of the standard model. Such inhomogeneities may thus affect the dynamics of the subsequent quark-hadron phase transition.

We apply a functional perturbative approach to the calculation of the equal-time two-point correlation functions and the potential between static color charges to oneloop order in Coulomb gauge Yang-Mills theory. The functional approach proceeds through a solution of the Schrödinger equation for the vacuum wave functional to order g 2 and derives the equal-time correlation functions from a functional integral representation via new diagrammatic rules. We show that the results coincide with those obtained from the usual Lagrangian functional integral approach, extract the beta function, and determine the anomalous dimensions of the equal-time gluon and ghost two-point functions and the static potential under the assumption of multiplicative renormalizability to all orders. *

We describe a technically very simple analytical approach to the deep infrared regime of Yang–Mills theory in the Landau gauge via Callan–Symanzik renormalization group equations in an epsilon expansion. This approach recovers all the solutions for the infrared gluon and ghost propagators previously found by solving the Dyson–Schwinger equations of the theory and singles out the solution with decoupling behavior, confirmed by lattice calculations, as the only one corresponding to an infrared attractive fixed point (for space-time dimensions above two). For the case of four dimensions, we describe the crossover of the system from the ultraviolet to the infrared fixed point and determine the complete momentum dependence of the propagators. The results for different renormalization schemes are compared to the lattice data.

We review the evolution of a spatially homogeneous and isotropic universe described by a Friedmann-Robertson-Walker spacetime filled with a collisionless, neutral, simple, massive gas. The gas is described by a one-particle distribution function which satisfies the Liouville equation and is assumed to be homogeneous and isotropic. Making use of the isometries of the spacetime, we define precisely the homogeneity and isotropicity property of the distribution function, and based on this definition we give a concise derivation of the most general family of such distribution functions. For this family, we construct the particle current density and the stress-energy tensor and consider the coupled Einstein-Liouville system of equations. We find that as long as the distribution function is collisionless, homogenous and isotropic, the evolution of a Friedmann-Robertson-Walker universe exhibits a singular origin. Its future development depends upon the curvature of the spatial sections: spatially flat or hyperboloid universes expand forever and this expansion dilutes the energy density and pressure of the gas, while a universe with compact spherical sections reaches a maximal expansion, after which it reverses its motion and recollapses to a final crunch singularity where the energy density and isotropic pressure diverge. Finally, we analyze the evolution of the universe filled with the collisionless gas once a cosmological constant is included.

We analyse the unification parameters MGUT and 1/ alpha GUT as functions of the numbers of fermion families (F) and Higgs doublets (H and HSUSY) within the standard model embedded in SU(5) and SUSY SU(5). Analytical (where possible) and numerical solutions to first- and second-order approximations of the evolution equation for the couplings alpha i are considered. As a result, restrictions on the unification parameters constrain F, H and HSUSY in such a way that SU(5) is ruled out by constraints on H, and F is severely limited in SUSY SU(5).