Semiclassical transition probabilities for interacting oscillators

Semiclassical transition probabilities characterize transfer of energy between "hard" and "soft" modes in various physical systems. We establish the boundary problem for singular euclidean solutions used to calculate such probabilities. Solutions are found numerically for a system of two interacting quartic oscillators. In the double-well case, we find numerical evidence that certain regular {\em minkowskian} trajectories have approximate stopping points or, equivalently, are approximately periodic. This property leads to estimates of tunneling excitation probabilities in that system and suggests that similar estimates may be possible in other systems with tunneling.Comment: 19 pages, LATEX, PURD-TH-94-03 (adds estimates of accuracy of numerical calculations

Cosmic microwave background and parametric resonance in reheating

The variation of the perturbative 3-curvature parameter, \zeta, is investigated in the period of reheating after inflation. The two-field model used has the inflaton, with an extra scalar field coupled to it, and non-linear effects of both fields are included as well as a slow decay mechanism into the hydrodynamic fluid of the radiation era. Changes in \zeta occur and persist into the succeeding cosmic eras to influence the generation of the cosmic microwave background fluctuations.Comment: 21 pages, 6 figures.Corrects misprinted formula and 2 number

Topological Defects Formation after Inflation on Lattice Simulation

We consider the formation of topological defects after inflation. In order to take into account the effects of the rescattering of fluctuations, we integrate the classical equation that describes the evolution of a complex scalar field on the two-dimensional lattice with a slab symmetry. The growth of fluctuations during preheating is found not to be enough for defect formation, and rather a long stage of the rescattering of fluctuations after preheating is necessary. We conclude that the topological defects are not formed if the breaking scale \eta is lager than \sim (2 - 3)\times 10^{16} GeV.Comment: 7 pages, RevTex, 10 postscript figures included; version to be published in Phys. Rev.

The Universe after inflation: the wide resonance case

We study numerically the decay of massive and massless inflatons into massive excitations, via a $\phi^2 X^2$ coupling, in the expanding Universe. We find that a wide enough resonance can survive the Universe expansion, though account for the expansion is very important for determining precisely how wide it should be. For a massive inflaton, the effective production of particles with mass ten times that of the inflaton requires very large values of the resonance parameter $q$, q\gsim 10^8. For these large $q$, the maximal size of produced fluctuations is significantly suppressed by the back reaction, but at least within the Hartree approximation they are still not negligible. For the massless inflaton with a $\lambda\phi^4/4$ potential, the Universe expansion completely prevents a resonance production of particles with masses larger than $\sqrt{\lambda}\phi(0)$ for $q$ up to $q=10^6$.Comment: LaTeX, 12 pages including 3 figure

Domain Wall Production During Inflationary Reheating

We numerically investigate the decay, via parametric resonance, of the inflaton with an m^2 phi^2 potential into a scalar matter field with a symmetry breaking potential. We consider the case where symmetry breaking takes place during inflation. We show that when expansion is not taken into account symmetry restoration and non-thermal defect production during reheating is possible. However in an expanding universe the fields do not spend sufficient time in the instability bands; thus symmetry restoration and subsequent domain wall production do not occur.Comment: 6 pages, 5 figure

Reheating and thermalization in a simple scalar model

We consider a simple model for the Universe reheating, which consists of a single self--interacting scalar field in Minkowskian space--time. Making use of the existence of an additional small parameter proportional to the amplitude of the initial spatially homogeneous field oscillations, we show that the behavior of the field can be found reliably. We describe the evolution of the system from the homogeneous oscillations to the moment when thermalization is completed. We compare our results with the Hartree--Fock approximation and argue that some properties found for this model may be the common features of realistic theories.Comment: Some changes in Introduction and Discussion, comparison with the Hartree--Fock results added. 37 pages, 2 postscript figures attache

Instanton propagator and instanton induced processes in scalar model

The propagator in the instanton background in the $(- \lambda \phi^{4})$ scalar model in four dimensions is studied.Leading and sub-leading terms of its asymptotics for large momenta and its on-shell double residue are calculated analytically. These results are applied to the analysis of the initial-state and initial-final-state corrections and the calculation of the next-to-leading (propagator) correction to the exponent of the cross section of instanton induced multiparticle scattering processes.Comment: 44 pages, 7 postscript figures, LaTe

Q-ball Formation through Affleck-Dine Mechanism

We present the full nonlinear calculation of the formation of a Q-ball through the Affleck-Dine (AD) mechanism by numerical simulations. It is shown that large Q-balls are actually produced by the fragmentation of the condensate of a scalar field whose potential is very flat. We find that the typical size of a Q-ball is determined by the most developed mode of linearized fluctuations, and almost all the initial charges which the AD condensate carries are absorbed into the formed Q-balls, whose sizes and the charges depend only on the initial charge densities.Comment: 4 pages, RevTex, 3 postscript figures included, the published versio

Parity Violating Bosonic Loops at Finite Temperature

The finite temperature parity-violating contributions to the polarization tensor are computed at one loop in a system without fermions. The system studied is a Maxwell-Chern-Simons-Higgs system in the broken phase, for which the parity-violating terms are well known at zero temperature. At nonzero temperature the static and long-wavelength limits of the parity violating terms have very different structure, and involve non-analytic log terms depending on the various mass scales. At high temperature the boson loop contribution to the Chern-Simons term goes like T in the static limit and like T log T in the long-wavelength limit, in contrast to the fermion loop contribution which behaves like 1/T in the static limit and like log T/T in the long wavelength limit.Comment: 10 pp, 1 fig, revte

Chern-Simons production during preheating in hybrid inflation models

We study the onset of symmetry breaking after hybrid inflation in a model having the field content of the SU(2) gauge-scalar sector of the standard model, coupled to a singlet inflaton. This process is studied in (3+1)-dimensions in a fully non-perturbative way with the help of lattice techniques within the classical approximation. We focus on the role played by gauge fields and, in particular, on the generation of Chern-Simons number. Our results are shown to be insensitive to the various cut-offs introduced in our numerical approach. The spectra preserves a large hierarchy between long and short-wavelength modes during the whole period of symmetry breaking and Chern-Simons generation, confirming that the dynamics is driven by the low momentum sector of the theory. We establish that the Chern-Simons production mechanism is associated with local sphaleron-like structures. The corresponding sphaleron rates are of order 10^{-5} m^4, which, within certain scenarios of electroweak baryogenesis and a (not unnaturally large) additional source of CP violation, could explain the present baryon asymmetry of the universe.Comment: 28 pages, 15 figures, ReVTeX. With minor corrections, version to appear in Phys. Rev.