Remarks on Cosmic String Formation during Preheating on Lattice Simulations

We reconsider the formation of (global) cosmic strings during and after preheating by calculating the dynamics of a scalar field on both two- and three- dimensional lattices. We have found that there is little differences between the results in two and three dimensions about the dynamics of fluctuations, at least, during preheating. Practically, it is difficult to determine whether long cosmic strings which may affect the later evolution of the universe could ever be produced from the results of simulations on three-dimensional lattices with smaller box sizes than the horizon. Therefore, using two-dimensional lattices with large box size, we have found that cosmic strings with the breaking scale 0\eta \sim 10^{16} GeV are produced for broad range of parameter space in \eta, while for higher breaking scales (\eta \sim 3\times 10^{16} GeV), their production depends crucially on the value of the breaking scale \eta in our simulations.Comment: 7 pages, RevTex, 14 postscript figures included, to appear in Phys. Rev.

First-order nonthermal phase transition after preheating

During preheating after inflation, parametric resonance rapidly generates very large fluctuations of scalar fields. In models where the inflaton field $\phi$ oscillates in a double-well potential and interacts with another scalar field $X$, fluctuations of X can keep the \phi to -\phi symmetry temporarily restored. If the coupling of \phi to X is much stronger than the inflaton self-coupling, the subsequent symmetry breaking is a first-order phase transition. We demonstrate the existence of this nonthermal phase transition with lattice simulations of the full nonlinear dynamics of the interacting fields. In particular, we observe nucleation of an expanding bubble.Comment: RevTeX, 4 page

Evolution of the Order Parameter after Bubble Collisions

If a first-order phase transition is terminated by collisions of new-phase bubbles, there will exist a period of nonequilibrium between the time bubbles collide and the time thermal equilibrium is established. We study the behavior of the order parameter during this phase. We find that large nonthermal fluctuations at this stage tend to restore symmetry, i.e., the order parameter is smaller than its eventual thermal equilibrium value. We comment on possible consequences for electroweak baryogenesis.Comment: 11 page LaTeX file with two figures, fig1.ps and fig2.p

Resonant Production of Topological Defects

We describe a novel phenomenon in which vortices are produced due to resonant oscillations of a scalar field which is driven by a periodically varying temperature T, with T remaining much below the critical temperature $T_c$. Also, in a rapid heating of a localized region to a temperature {\it below} $T_c$, far separated vortex and antivortex can form. We compare our results with recent models of defect production during reheating after inflation. We also discuss possible experimental tests of our predictions of topological defect production {\it without} ever going through a phase transition.Comment: Revtex, 13 pages including 5 postscript figure

Patterns from preheating

The formation of regular patterns is a well-known phenomenon in condensed matter physics. Systems that exhibit pattern formation are typically driven and dissipative with pattern formation occurring in the weakly non-linear regime and sometimes even in more strongly non-linear regions of parameter space. In the early universe, parametric resonance can drive explosive particle production called preheating. The fields that are populated then decay quantum mechanically if their particles are unstable. Thus, during preheating, a driven-dissipative system exists. In this paper, we show that a self-coupled inflaton oscillating in its potential at the end of inflation can exhibit pattern formation.Comment: 4 pages, RevTex, 6 figure

Resonant decay of Bose condensates

We present results of fully non-linear calculations of decay of the inflaton interacting with another scalar field X. Combining numerical results for cosmologically interesting range of resonance parameter, q \leq 10^6, with analytical estimates, we extrapolate them to larger q. We find that scattering of X fluctuations off the Bose condensate is a very efficient mechanism limiting growth of X fluctuations. For a single-component X, the resulting variance, at large q, is much smaller than that obtained in the Hartree approximation.Comment: LaTeX, 10 pages including 4 figure

Baryon number non-conservation and phase transitions at preheating

Certain inflation models undergo pre-heating, in which inflaton oscillations can drive parametric resonance instabilities. We discuss several phenomena stemming from such instabilities, especially in weak-scale models; generically, these involve energizing a resonant system so that it can evade tunneling by crossing barriers classically. One possibility is a spontaneous change of phase from a lower-energy vacuum state to one of higher energy, as exemplified by an asymmetric double-well potential with different masses in each well. If the lower well is in resonance with oscillations of the potential, a system can be driven resonantly to the upper well and stay there (except for tunneling) if the upper well is not resonant. Another example occurs in hybrid inflation models where the Higgs field is resonant; the Higgs oscillations can be transferred to electroweak (EW) gauge potentials, leading to rapid transitions over sphaleron barriers and consequent B+L violation. Given an appropriate CP-violating seed, we find that preheating can drive a time-varying condensate of Chern-Simons number over large spatial scales; this condensate evolves by oscillation as well as decay into modes with shorter spatial gradients, eventually ending up as a condensate of sphalerons. We study these examples numerically and to some extent analytically. The emphasis in the present paper is on the generic mechanisms, and not on specific preheating models; these will be discussed in a later paper.Comment: 10 pages, 7 figures included, revtex, epsf, references adde

Structure of Resonance in Preheating after Inflation

We consider preheating in the theory $1/4 \lambda \phi^4 + 1/2 g^2\phi^2\chi^2$, where the classical oscillating inflaton field $\phi$ decays into $\chi$-particles and $\phi$-particles. The parametric resonance which leads to particle production in this conformally invariant theory is described by the Lame equation. It significantly differs from the resonance in the theory with a quadratic potential. The structure of the resonance depends in a rather nontrivial way on the parameter $g^2/\lambda$. We construct the stability/instability chart in this theory for arbitrary $g^2/\lambda$. We give simple analytic solutions describing the resonance in the limiting cases $g^2/\lambda\ll 1$ and $g^2/\lambda \gg 1$, and in the theory with $g^2=3\lambda$, and with $g^2 =\lambda$. From the point of view of parametric resonance for $\chi$, the theories with $g^2=3\lambda$ and with $g^2 =\lambda$ have the same structure, respectively, as the theory $1/4 \lambda \phi^4$, and the theory $\lambda /(4 N) (\phi^2_i)^2$ of an N-component scalar field $\phi_i$ in the limit $N \to \infty$. We show that in some of the conformally invariant theories such as the simplest model $1/4 \lambda\phi^4$, the resonance can be terminated by the backreaction of produced particles long before $$or$$ become of the order $\phi^2$. We analyze the changes in the theory of reheating in this model which appear if the inflaton field has a small mass.Comment: 19 pages, revtex, 12 figure

Gamma photons from parametric resonance in neutron stars

Shock waves in cold nuclear matter, e.g. those induced by a collision of two neutron stars, can generate a large number of gamma photons via parametric resonance. We study the resonant production of gamma rays inside a shocked neutron star and discuss the possible astrophysical consequences of this phenomenon.Comment: 5 pages, ReVTeX, 5 figures inserted with epsf; replaced with a final version (minor changes

Renormalization of nonequilibrium dynamics in FRW cosmology

We derive the renormalized nonequilibrium equations of motion for a scalar field and its quantum back reaction in a conformally flat Friedmann-Robertson-Walker universe. We use a fully covariant formalism proposed by us recently for handling numerically and analytically nonequilibrium dynamics in one-loop approximation. The system is assumed to be in a conformal vacuum state initially. We use dimensional regularization; we find that the counter terms can be chosen independent of the initial conditions though the divergent leading order graphs do depend on them.Comment: 14 pages, RevTeX, some obvious typos correcte