Defect formation and critical dynamics in the early Universe - art. no. 045009

We study the nonequilibrium dynamics leading to the formation of topologica l defects in a symmetry breaking phase transition of a quantum scalar field with lambda Phi(4) self-interaction in a spatially flat, radiation-dominat ed Friedmann-Robertson-Walker universe. The quantum field is initially in a finite-temperature symmetry-restored state and the phase transition develo ps as the universe expands and cools. We present a first-principles, micros copic approach in which the nonperturbative, nonequilibrium dynamics of the quantum field is derived from the two-loop, two-particle-irreducible close d-time-path effective action. We numerically solve the dynamical equations for the two-point function and we identify signatures of correlated domains in the infrared portion of the momentum-space power spectrum. We find that correlated domains formed during the phase transition scale in size as a p ower law with the expansion rate of the universe. We calculate the equilibr ium critical exponents of the correlation length and relaxation time for th is model and show that the power law exponent of the domain size, for both overdamped and underdamped evolution, is in good agreement with the ''freez e-out'' scenario proposed by Zurek. We introduce an analytic dynamical mode l, valid near the critical point, that exhibits the same power-law scaling of the size of correlated domains with the quench rate. The size of correla ted domains provides an approximate measure of the initial scale of the top ological defect density. By incorporating the realistic quench of the expan ding universe our approach illuminates the dynamical mechanisms important f or topological defect formation, and provides a preliminary step towards a complete and rigorous picture of defect formation in a second-order phase t ransition of a quantum field. The observed power law scaling of the size of correlated domains with the quench rate, calculated here in a quantum fiel d theory context, provides evidence for the ''freeze-out" scenario in three spatial dimensions. [S0556-2821(99)02902-1].