Pattern Formation in the Early Universe

Systems that exhibit pattern formation are typically driven and dissipative. 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. We have shown previously that pattern formation can occur in two dimensions in a self-coupled inflaton system undergoing parametric resonance. In this paper, we provide evidence of pattern formation for more realistic initial conditions in both two and three dimensions. In the one-field case, we have the novel interpretation that these patterns can be thought of as a network of domain walls. We also show that the patterns are spatio-temporal, leading to a distinctive, but probably low-amplitude peak in the gravitational wave spectrum. In the context of a two-field model, we discuss putting power from resonance into patterns on cosmological scales, in particular to explain the observed excess power at 100 h^{-1}Mpc, but why this seems unlikely in the absence of a period of post-preheating inflation. Finally we note our model is similar to that of the decay of DCCs and therefore pattern formation may also occur at RHIC and LHC.Comment: 9 pages, 11 figure

Primordial Non-Gaussianity: Baryon Bias and Gravitational Collapse of Cosmic String Wakes

I compute the 3-D non-linear evolution of gas and dark matter fluids in the neighbourhood of cosmic string wakes which are formed at high redshift ($z\simeq 2240$) for a ``realistic'' scenario of wake formation. These wakes are the ones which stand out most prominently as cosmological sheets and are expected to play a dominant r\^ole in the cosmic string model of structure formation. Employing a high-resolution 3-D hydrodynamics code to evolve these wakes until the present day yields results for the baryon bias generated in the inner wake region. I find that today, wakes would be $1.5 h^{-1}$ Mpc thick and contain a 70% excess in the density of baryons over the dark matter density in their centre. However, high density peaks in the wake region do not inherit a baryon enhancement. I propose a mechanism for this erasure of the baryon excess in spherically collapsed objects based on the geometry change around the collapsing region. Further, I present heuristic arguments for the consequences of this work for large scale structure in the cosmic string model and conclude that the peculiarities of wake formation are unlikely to have significant import on the discrepancy between power spectrum predictions and observations in this model. If one invokes the nucleosynthesis bound on $\Omega_b$ this could be seen as strengthening the case against $\Omega_m=1$ or for low Hubble constants.Comment: 21 pages, 7 figures, 2 tables, prepared with the AASTeX package. Minor modifications, results unchanged. ApJ in press, scheduled for Vol. 50

Collapse of topological texture

We study analytically the process of a topological texture collapse in the approximation of a scaling ansatz in the nonlinear sigma-model. In this approximation we show that in flat space-time topological texture eventually collapses while in the case of spatially flat expanding universe its fate depends on the rate of expansion. If the universe is inflationary, then there is a possibility that texture will expand eternally; in the case of exponential inflation the texture may also shrink or expand eternally to a finite limiting size, although this behavior is degenerate. In the case of power law noninflationary expansion topological texture eventually collapses. In a cold matter dominated universe we find that texture which is formed comoving with the universe expansion starts collapsing when its spatial size becomes comparable to the Hubble size, which result is in agreement with the previous considerations. In the nonlinear sigma-model approximation we consider also the final stage of the collapsing ellipsoidal topological texture. We show that during collapse of such a texture at least two of its principal dimensions shrink to zero in a similar way, so that their ratio remains finite. The third dimension may remain finite (collapse of cigar type), or it may also shrink to zero similar to the other two dimensions (collapse of scaling type), or shrink to zero similar to the product of the remaining two dimensions (collapse of pancake type).Comment: 23 pages, LaTeX, to be published in Phys. Rev.

The bispectrum of matter perturbations from cosmic strings

We present the first calculation of the bispectrum of the matter perturbations induced by cosmic strings. The calculation is performed in two different ways: the first uses the unequal time correlators (UETCs) of the string network - computed using a Gaussian model previously employed for cosmic string power spectra. The second approach uses the wake model, where string density perturbations are concentrated in sheet-like structures whose surface density grows with time. The qualitative and quantitative agreement of the two gives confidence to the results. An essential ingredient in the UETC approach is the inclusion of compensation factors in the integration with the Green's function of the matter and radiation fluids, and we show that these compensation factors must be included in the wake model also. We also present a comparison of the UETCs computed in the Gaussian model, and those computed in the unconnected segment model (USM) used by the standard cosmic string perturbation package CMBACT. We compare numerical estimates for the bispectrum of cosmic strings to those produced by perturbations from an inflationary era, and discover that, despite the intrinsically non-Gaussian nature of string-induced perturbations, the matter bispectrum is unlikely to produce competitive constraints on a population of cosmic strings

A Semi-Analytical Analysis of Texture Collapse

This study presents a simplified approach to studying the dynamics of global texture collapse. We derive equations of motion for a spherically symmetric field configuration using a two parameter ansatz. Then we analyse the effective potential for the resulting theory to understand possible trajectories of the field configuration in the parameter space of the ansatz. Numerical results are given for critical winding and collapse time in spatially flat non-expanding, and flat expanding universes. In addition, the open non-expanding and open-expanding cases are studied.Comment: 12 pages, figures available from author, BROWN-HET-895, uses phyzz