First Order Phase Transitions in the Early Universe

Details First Order Phase Transitions in the Early Universe First Order Phase Transitions in the Early Universe

Jan 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996phdt.........4f&link_type=abstract

Thesis (PH.D.)--TUFTS UNIVERSITY, 1996.Source: Dissertation Abstracts International, Volume: 57-04, Section: B, page: 2618.

Mathematics

Probability

Bubble Nucleation, Cosmology

Scientific paper

First order phase transitions occur via nucleation of bubbles of the new phase (true vacuum) in the old phase (false vacuum). The technique most widely used to compute the probability of bubble nucleation in a field theory phase transition is based on instanton methods in the context of the semiclassical approximation. At zero temperature in 3+1 dimensions the nucleation rate is dominated by the O(4) symmetric instanton, a sphere of radius R, while at temperatures TggR^ {-1} the decay is dominated by a "cylindrical" (static) instanton with O(3) invariance. There has been discussion in the literature as to whether the transition between these two regimens would be first order (discontinuity in the first derivative of the nucleation rate at the transition temperature Tc), or second order (continuity of the first derivative, but discontinuity of the second derivative at Tc). In the first part of the thesis we obtain the finite temperature solutions corresponding to the quantum and the thermal regimes, and compute their action as a function of the temperature for different values of the wall thickness in a varphi^4 potential, as a toy model for a transition in the early universe. Our results indicate that only for the cases of very large wall thickness a second order transition takes place, while for all the other cases a first order transition occurs. We also study the 2+l and l+l dimensional cases in two condensed matter cases. In the second part of the thesis we study the collision process for vacuum bubbles expanding in a plasma. The effects of the plasma are simulated by introducing a damping term in the equations of motion for a U(1) global field. We find that Lorentz-contracted spherically symmetric domain walls adequately describe the overdamped motion of the bubbles in the thin wall approximation, and study the process of collision and phase equilibration both numerically and analytically. With an analytical model for the phase propagation in 1+1 dimensions, we prove that the phase waves generated in the bubble merging are reflected by the walls of the true vacuum cavity, giving rise to a long-lived oscillating state that delays the phase equilibration. The existence of such a state in the 3+1 dimensional model is then confirmed by numerical simulations, and the consequences for the formation of vortices in three-bubble collisions are considered.

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