Defect formation and critical dynamics in the early Universe

Abstract

We study the nonequilibrium dynamics leading to the formation of topological defects in a symmetry-breaking phase transition of a quantum scalar field with λΦ 4 self-interaction in a spatially flat, radiation-dominated Friedmann-Robertson Walker Universe. The quantum field is initially in a finitetemperature symmetry-restored state and the phase transition develops as the Universe expands and cools. We present a first-principles, microscopic approach in which the nonperturbative, nonequilibrium dynamics of the quantum field is derived from the two-loop, two-particle-irreducible closed-timepath effective action. We numerically solve the dynamical equations for the two-point function and we identify signatures of topological defects in the infrared portion of the momentum-space power spectrum. We find that the density of topological defects formed after the phase transition scales as a power law with the expansion rate of the universe. We calculate the equilibrium critical exponents of the correlation length and relaxation time for this model and show that the power law exponent of the defect density, for both overdamped and underdamped evolution, is in good agreement with the "freeze-out" scenario proposed by Zurek. We also introduce an analytic dynamical model, valid near the critical point, that exhibits the same power-law scaling of the defect density with the quench rate. By incorporating the realistic quench of the expanding Universe our approach illuminates the dynamical mechanisms important for topological defect formation and provides a preliminary step towards a complete and rigorous picture of defect formation * Electronic address:

The Onset of Phase Transitions in Condensed Matter and Relativistic QFT

“…There are several possible approaches. One step is to take the FRW metric of the early universe seriously, whereby the dissipation due to the expansion of the universe can change the situation dramatically [36]. Other approaches are more explicit in their attempts to trigger decoherence explicitly, as we mentioned earlier.…”

“…As a path integral 36) where S t [φ] is the (time-dependent) action that describes how the field φ is driven by the environment and spatial and field labels have been suppressed (e.g. Dφ = Dφ 1 Dφ 2 ).…”

Effects of multiplicative noise in relativistic phase transitions

“…In practice, an ab initio calculation from the microscopic field dynamics suggests the validity of the scaling laws, but does not permit an estimate of the efficiency of defect production outside the framework of mean-field (or large-N) approximations [9,10].…”

How Phase Transitions Induce Classical Behaviour

“…With this choice the effect of the φ-field on the χ a thermal masses is, relatively, O(1/ √ N ) and can be ignored. We stress that this is not a Hartree or large-N approximation of the type that, to date, has been the main way to proceed [24,25,26] for a closed system.…”