Dynamics of symmetry breaking in FRW cosmologies: Emergence of scaling - art. no. 105014

The dynamics of a symmetry breaking phase transition is studied in a radiat ion and matter dominated spatially Bat FRW cosmology in the large N limit o f a scalar field theory. The quantum density matrix is evolved from an init ial stare of quasiparticles in thermal equilibrium at a temperature higher than the critical. The cosmological expansion decreases the temperature and triggers the phase transition. We identify three different time scales: an early regime dominated by linear instabilities and the exponential growth of long wavelength fluctuations, an intermediate scale when the field fluct uations probe the broken symmetry states and an asymptotic scale wherein a scaling regime emerges fur modes of wavelength comparable to or larger than the horizon. The scaling regime is characterized by a dynamical physical c orrelation length xi(phys) = d(H)(t) with d(H)(t) the size of the causal ho rizon; thus there is one correlated region pet causal horizon. inside these correlated regions the field fluctuations sample the broken symmetry state s. The amplitude of the long-wavelength fluctuations becomes non-perturbati vely large due to the early times instabilities and a semiclassical bur sto chastic description emerges in the asymptotic regime. Tn the scaling regime , the power spectrum is peaked at zero momentum revealing the onset of a Bo se-Einstein condensate. The scaling solution results in that the equation o f state of the scalar fields is the same as that of the background fluid. T his implies a Harrison-Zeldovich spectrum of scalar density perturbations f or long-wavelengths. We discuss the corrections to scaling as well as the u niversality of the scaling solution and the differences and similarities wi th the classical non-linear sigma model.