Caustics in Tachyon Matter and Other Born-Infeld Scalars

We consider scalar Born-Infeld type theories with arbitrary potentials V(T) of a scalar field T. We find that for models with runaway potentials V(T) the generic inhomogeneous solutions after a short transient stage can be very well approximated by the solutions of a Hamilton-Jacobi equation that describes free streaming wave front propagation. The analytic solution for this wave propagation shows the formation of caustics with multi-valued regions beyond them. We verified that these caustics appear in numerical solutions of the original scalar BI non-linear equations. Our results include the scalar BI model with an exponential potential, which was recently proposed as an effective action for the string theory tachyon in the approximation where high-order spacetime derivatives of T are truncated. Since the actual string tachyon dynamics contain derivatives of all orders, the tachyon BI model with an exponential potential becomes inadequate when the caustics develop because high order spatial derivatives of T become divergent. BI type tachyon theory with a potential decreasing at large T could have interesting cosmological applications because the tachyon field rolling towards its ground state at infinity acts as pressureless dark matter. We find that inhomogeneous cosmological tachyon fluctuations rapidly grow and develop multiple caustics. Any considerations of the role of the tachyon field in cosmology will have to involve finding a way to predict the behavior of the field at and beyond these caustics

Inhomogeneous Fragmentation of the Rolling Tachyon

Dirac-Born-Infeld type effective actions reproduce many aspects of string theory classical tachyon dynamics of unstable Dp-branes. The inhomogeneous tachyon field rolling from the top of its potential forms topological defects of lower codimensions. In between them, as we show, the tachyon energy density fragments into a p-dimensional web-like high density network evolving with time. We present an analytic asymptotic series solution of the non-linear equations for the inhomogeneous tachyon and its stress energy. The generic solution for a tachyon field with a runaway potential in arbitrary dimensions is described by the free streaming of noninteracting massive particles whose initial velocities are defined by the gradients of the initial tachyon profile. Thus, relativistic particle mechanics is a dual picture of the tachyon field effective action. Implications of this picture for inflationary models with a decaying tachyon field are discussed.Comment: 10 pages, 1 figur

Dynamics of Symmetry Breaking and Tachyonic Preheating

We reconsider the old problem of the dynamics of spontaneous symmetry breaking using 3d lattice simulations, and develop a theory of tachyonic preheating, which occurs due to the spinodal instability of the scalar field. Tachyonic preheating is so efficient that symmetry breaking typically completes within a single oscillation of the field distribution as it rolls towards the minimum of its effective potential. As an application of this theory we consider preheating in the hybrid inflation scenario, including SUSY-motivated F-term and D-term inflationary models. We show that preheating in hybrid inflation is typically tachyonic and the stage of oscillations of a homogeneous component of the scalar fields driving inflation ends after a single oscillation. Our results may also be relevant for the theory of the formation of disoriented chiral condensates in heavy ion collisions.Comment: 7 pages, 6 figures. Higher quality figures and computer generated movies in gif format illustrating our results can be found at http://physics.stanford.edu/gfelder/hybri

Chaos and Preheating

We show evidence for a relationship between chaos and parametric resonance both in a classical system and in the semiclassical process of particle creation. We apply our considerations in a toy model for preheating after inflation.Comment: 7 pages, 9 figures; uses epsfig and revtex v3.1. Matches version accepted for publication in Phys. Rev.

Preheating in Supersymmetric Theories

We examine the particle production via preheating at the end of inflation in supersymmetric theories. The inflaton and matter scalars are now necessarily complex fields, and their relevant interactions are restricted by holomorphy. In general this leads to major changes both in the inflaton dynamics and in the efficiency of the preheating process. In addition, supersymmetric models generically contain multiple isolated vacua, raising the possibility of non-thermal production of dangerous topological defects. Because of these effects, the success of leptogenesis or WIMPZILLA production via preheating depends much more sensitively on the detailed parameters in the inflaton sector than previously thought.Comment: 24 pages, 3 figures; references adde

New bulk scalar field solutions in brane worlds

We use nonlinear perturbation theory to obtain new solutions for brane world models that incorporate a massive bulk scalar field. We then consider tensor perturbations and show that Newtonian gravity is recovered on the brane for both a light scalar field and for a bulk field with large negative mass. This latter result points to the viability of higher-derivative theories of gravity in the context of bulk extra dimensions.Comment: 4+\epsilon pages, no 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

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

The Development of Equilibrium After Preheating

We present a fully nonlinear study of the development of equilibrium after preheating. Preheating is the exponentially rapid transfer of energy from the nearly homogeneous inflaton field to fluctuations of other fields and/or the inflaton itself. This rapid transfer leaves these fields in a highly nonthermal state with energy concentrated in infrared modes. We have performed lattice simulations of the evolution of interacting scalar fields during and after preheating for a variety of inflationary models. We have formulated a set of generic rules that govern the thermalization process in all of these models. Notably, we see that once one of the fields is amplified through parametric resonance or other mechanisms it rapidly excites other coupled fields to exponentially large occupation numbers. These fields quickly acquire nearly thermal spectra in the infrared, which gradually propagates into higher momenta. Prior to the formation of total equilibrium, the excited fields group into subsets with almost identical characteristics (e.g. group effective temperature). The way fields form into these groups and the properties of the groups depend on the couplings between them. We also studied the onset of chaos after preheating by calculating the Lyapunov exponent of the scalar fields.Comment: 15 pages, 23 figure