LATTICEEASY: A Program for Lattice Simulations of Scalar Fields in an Expanding Universe

We describe a C++ program that we have written and made available for calculating the evolution of interacting scalar fields in an expanding universe. The program is particularly useful for the study of reheating and thermalization after inflation. The program and its full documentation are available on the Web at http://physics.stanford.edu/gfelder/latticeeasy. In this paper we provide a brief overview of what the program does and what it is useful for

Black hole production in tachyonic preheating

We present fully non-linear simulations of a self-interacting scalar field in the early universe undergoing tachyonic preheating. We find that density perturbations on sub-horizon scales which are amplified by tachyonic instability maintain long range correlations even during the succeeding parametric resonance, in contrast to the standard models of preheating dominated by parametric resonance. As a result the final spectrum exhibits memory and is not universal in shape. We find that throughout the subsequent era of parametric resonance the equation of state of the universe is almost dust-like, hence the Jeans wavelength is much smaller than the horizon scale. If our 2D simulations are accurate reflections of the situation in 3D, then there are wide regions of parameter space ruled out by over-production of black holes. It is likely however that realistic parameter values, consistent with COBE/WMAP normalisation, are safetly outside this black hole over-production region.Comment: 6pages, 7figures, figures correcte

Preheating with Trilinear Interactions: Tachyonic Resonance

We investigate the effects of bosonic trilinear interactions in preheating after chaotic inflation. A trilinear interaction term allows for the complete decay of the massive inflaton particles, which is necessary for the transition to radiation domination. We found that typically the trilinear term is subdominant during early stages of preheating, but it actually amplifies parametric resonance driven by the four-legs interaction. In cases where the trilinear term does dominate during preheating, the process occurs through periodic tachyonic amplifications with resonance effects, which is so effective that preheating completes within a few inflaton oscillations. We develop an analytic theory of this process, which we call tachyonic resonance. We also study numerically the influence of trilinear interactions on the dynamics after preheating. The trilinear term eventually comes to dominate after preheating, leading to faster rescattering and thermalization than could occur without it. Finally, we investigate the role of non-renormalizable interaction terms during preheating. We find that if they are present they generally dominate (while still in a controllable regime) in chaotic inflation models. Preheating due to these terms proceeds through a modified form of tachyonic resonance.Comment: 19 pages, 10 figures, refs added, published versio

Preheating in Derivatively-Coupled Inflation Models

We study preheating in theories where the inflaton couples derivatively to scalar and gauge fields. Such couplings may dominate in natural models of inflation, in which the flatness of the inflaton potential is related to an approximate shift symmetry of the inflaton. We compare our results with previously studied models with non-derivative couplings. For sufficiently heavy scalar matter, parametric resonance is ineffective in reheating the universe, because the couplings of the inflaton to matter are very weak. If scalar matter fields are light, derivative couplings lead to a mild long-wavelength instability that drives matter fields to non-zero expectation values. In this case however, long-wavelength fluctuations of the light scalar are produced during inflation, leading to a host of cosmological problems. In contrast, axion-like couplings of the inflaton to a gauge field do not lead to production of long-wavelength fluctuations during inflation. However, again because of the weakness of the couplings to the inflaton, parametric resonance is not effective in producing gauge field quanta.Comment: 10 pages, 9 figure

Bose Einstein condensation at reheating

We discuss the possibility that a perturbative reheating stage after inflation produces a scalar particle gas in a Bose condensate state, emphasizing the possible cosmological role of this phenomenon for symmetry restoration.Comment: 4 pages, 4 figures. Revised version, with an improved analysis of the condensate formatio

Dynamics of tachyonic preheating after hybrid inflation

We study the instability of a scalar field at the end of hybrid inflation, using both analytical techniques and numerical simulations. We improve previous studies by taking the inflaton field fully into account, and show that the range of unstable modes depends sensitively on the velocity of the inflaton field, and thereby on the Hubble rate, at the end of inflation. If topological defects are formed, their number density is determined by the shortest unstable wavelength. Finally, we show that the oscillations of the inflaton field amplify the inhomogeneities in the energy density, leading to local symmetry restoration and faster thermalization. We believe this explains why tachyonic preheating is so effective in transferring energy away from the inflaton zero mode.Comment: 12 pages, 10 figures, REVTeX. Minor changes, some references added. To appear in PR

DEFROST: A New Code for Simulating Preheating after Inflation

At the end of inflation, dynamical instability can rapidly deposit the energy of homogeneous cold inflaton into excitations of other fields. This process, known as preheating, is rather violent, inhomogeneous and non-linear, and has to be studied numerically. This paper presents a new code for simulating scalar field dynamics in expanding universe written for that purpose. Compared to available alternatives, it significantly improves both the speed and the accuracy of calculations, and is fully instrumented for 3D visualization. We reproduce previously published results on preheating in simple chaotic inflation models, and further investigate non-linear dynamics of the inflaton decay. Surprisingly, we find that the fields do not want to thermalize quite the way one would think. Instead of directly reaching equilibrium, the evolution appears to be stuck in a rather simple but quite inhomogeneous state. In particular, one-point distribution function of total energy density appears to be universal among various two-field preheating models, and is exceedingly well described by a lognormal distribution. It is tempting to attribute this state to scalar field turbulence.Comment: RevTeX 4.0; 16 pages, 9 figure

Turbulent Thermalization

We study, analytically and with lattice simulations, the decay of coherent field oscillations and the subsequent thermalization of the resulting stochastic classical wave-field. The problem of reheating of the Universe after inflation constitutes our prime motivation and application of the results. We identify three different stages of these processes. During the initial stage of ``parametric resonance'', only a small fraction of the initial inflaton energy is transferred to fluctuations in the physically relevant case of sufficiently large couplings. A major fraction is transfered in the prompt regime of driven turbulence. The subsequent long stage of thermalization classifies as free turbulence. During the turbulent stages, the evolution of particle distribution functions is self-similar. We show that wave kinetic theory successfully describes the late stages of our lattice calculation. Our analytical results are general and give estimates of reheating time and temperature in terms of coupling constants and initial inflaton amplitude.Comment: 27 pages, 13 figure

Reconstruction of field theory from excitation spectra of defects

We show how to reconstruct a field theory from the spectrum of bound states on a topological defect. We apply our recipe to the case of kinks in 1+1 dimensions with one or two bound states. Our recipe successfully yields the sine-Gordon and $\lambda \phi^4$ field theories when suitable bound state spectra are assumed. The recipe can also be used to globally reconstruct the inflaton potential of inflationary cosmology if the inflaton produces a topological defect. We discuss how defects can provide ``smoking gun'' evidence for a class of inflationary models.Comment: 10 pages, 4 figures. Included proof (Appendix B) that wall fluctuation potentials have supersymmetric form. Added reference

Stochastic Gravitational Wave Production After Inflation

In many models of inflation, the period of accelerated expansion ends with preheating, a highly non-thermal phase of evolution during which the inflaton pumps energy into a specific set of momentum modes of field(s) to which it is coupled. This necessarily induces large, transient density inhomogeneities which can source a significant spectrum of gravitational waves. In this paper, we consider the generic properties of gravitational waves produced during preheating, perform detailed calculations of the spectrum for several specific inflationary models, and identify problems that require further study. In particular, we argue that if these gravitational waves exist they will necessarily fall within the frequency range that is feasible for direct detection experiments -- from laboratory through to solar system scales. We extract the gravitational wave spectrum from numerical simulations of preheating after $\lambda \phi^4$ and $m_{\phi}^2 \phi^2$ inflation, and find that they lead to a gravitational wave amplitude of around $\Omega_{gw}h^2\sim 10^{-10}$. This is considerably higher than the amplitude of the primordial gravitational waves produced during inflation. However, the typical wavelength of these gravitational waves is considerably shorter than LIGO scales, although in extreme cases they may be visible at scales accessible to the proposed BBO mission. We survey possible experimental approaches to detecting any gravitational wave background generated during preheating.Comment: 11 pages. Updated references. Minor clarification