122674580
Warped geometry of brane worlds
We study the dynamical equations for extra-dimensional dependence of a warp factor and a bulk scalar in 5D brane world scenarios with induced brane metric of constant curvature. These equations are similar to those for the time dependence of the scale factor and a scalar field in 4D cosmology, but with the sign of the scalar field potential reversed. Based on this analogy, we introduce novel methods for studying the warped geometry. We construct the full phase portraits of the warp factor/scalar system for several examples of the bulk potential. This allows us to view the global properties of the warped geometry. For flat branes, the phase portrait is two dimensional. Moving along typical phase trajectories, the warp factor is initially increasing and finally decreasing. All trajectories have timelike gradient-dominated singularities at one or both of their ends, which are reachable in a finite distance and must be screened by the branes. For curved branes, the phase portrait is three dimensional. However, as the warp factor increases the phase trajectories tend towards the two-dimensional surface corresponding to flat branes. We discuss this property as a mechanism that may stretch the curved brane to be almost flat, with a small cosmological constant. Finally, we describe the embedding of branes in the 5D bulk using the phase space geometric methods developed here. In this language the boundary conditions at the branes can be described as a 1D curve in the phase space. We discuss the naturalness of tuning the brane potential to stabilize the brane world system.
111386028
Theory and Numerics of Gravitational Waves from Preheating after Inflation
Preheating after inflation involves large, time-dependent field inhomogeneities, which act as a classical source of gravitational radiation. The resulting spectrum might be probed by direct detection experiments if inflation occurs at a low enough energy scale. In this paper, we develop a theory and algorithm to calculate, analytically and numerically, the spectrum of energy density in gravitational waves produced from an inhomogeneous background of stochastic scalar fields in an expanding universe. We derive some generic analytical results for the emission of gravity waves by stochastic media of random fields, which can test the validity/accuracy of numerical calculations. We contrast our method with other numerical methods in the literature, and then we apply it to preheating after chaotic inflation. In this case, we are able to check analytically our numerical results, which differ significantly from previous works. We discuss how the gravity-wave spectrum builds up with time and find that the amplitude and the frequency of its peak depend in a relatively simple way on the characteristic spatial scale amplified during preheating. We then estimate the peak frequency and amplitude of the spectrum produced in two models of preheating after hybrid inflation, which for some parameters may be relevant for gravity-wave interferometric experiments.
23586999
Microscopic calculations of low-energy reaction cross sections.
Microscopic calculations of nuclear reaction cross sections and total reaction probabilities are compared with measurements for the {ital d}+Si, {sup 3,4}He+Si, and {ital d}+Ge systems at energies ranging from 2 to 53 MeV/nucleon. Good agreement is obtained, except for {sup 3}He+Si at the very lowest energies, when zero-range nucleon-nucleon forces are assumed and realistic nuclear density distributions are used in the tail regions, where the models are most sensitive. The agreement is less good for finite-range forces. A strong absorption model gives much poorer agreement with the recent {sup 4}He+Si measurements than do the microscopic models.
118438589
From preheating to thermal equilibrium nonlinear dynamics of interacting fields
This paper presents the first fully nonlinear study of the development of equilibrium after preheating. Preheating is the exponentially rapid transfer of energy from the nearly homogeneous inflation field to fluctuations of the inflation itself and/or other fields. 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 these fields during and after preheating for a variety of inflationary models. We describe a number of generic features that govern the thermalization process in all of these models. Notably, we see that once a single field is amplified through parametric resonance or other mechanisms it rapidly excites other fields to exponentially large occupation numbers. All of these fields quickly acquire nearly thermal spectra in the infrared and then begin to gradually scatter their energy into higher momentum modes, thus bringing the spectra into thermal equilibrium.
6955171
Inhomogeneous Fragmentation of the Rolling Tachyon
Dirac-Born-Infeld type effective actions reproduce many aspects of string theory classical tachyon dynamics of unstable $\mathrm{D}p$-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 nonlinear 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.
122808897
Inflation after preheating
Preheating after inflation may lead to nonthermal phase transitions with symmetry restoration. These phase transitions may occur even if the total energy density of fluctuations produced during reheating is relatively small as compared with the vacuum energy in the state with restored symmetry. As a result, in some inflationary models one may encounter a secondary stage of inflation after preheating.
119590296
Differential Equations Compatible with KZ Equations
We define a system of ‘dynamical’ differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables zi taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the ‘dual’ variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions.