Woei Chet Lim

Asymptotic Silence of Generic Cosmological Singularities

In this Letter we investigate the nature of generic cosmological singularities using the framework developed by Uggla et al. We study the past asymptotic dynamics of general vacuum G2 cosmologies, which are expected to capture the singular behavior of generic cosmologies with no symmetries at all. Our results indicate that asymptotic silence holds, i.e., particle horizons along all time lines shrink to zero for generic solutions. Moreover, we provide evidence that spatial derivatives become dynamically insignificant along generic time lines, and that the evolution into the past along such time lines is governed by an asymptotic dynamical system which is associated with an invariant set-the silent boundary. We identify an attracting subset on the silent boundary that organizes the oscillatory dynamics of generic time lines in the singular regime. Finally, we discuss the dynamics associated with recurring spike formation.

Evolution to a smooth universe in an ekpyrotic contracting phase with w>1

A period of slow contraction with equation of state w> 1, known as an ekpyrotic phase, has been shown to flatten and smooth the universe if it begins the phase with small perturbations. In this paper, we explore how robust and powerful the ekpyrotic smoothing mechanism is by beginning with highly inhomogeneous and anisotropic initial conditions and numerically solving for the subsequent evolution of the universe. Our studies, based on a universe with gravity plus a scalar field with a negative exponential potential, show that some regions become homogeneous and isotropic while others exhibit inhomogeneous and anisotropic behavior in which the scalar field behaves like a fluid with w ¼ 1. We find that the ekpyrotic smoothing mechanism is robust in the sense that the ratio of the proper volume of the smooth to nonsmooth region grows exponentially fast along time slices of constant mean curvature.

Asymptotic isotropization in inhomogeneous cosmology

In this paper we investigate asymptotic isotropization. We derive the asymptotic dynamics of spatially inhomogeneous cosmological models with a perfect fluid matter source and a positive cosmological constant near the de Sitter equilibrium state at late times, and near the flat FL equilibrium state at early times. Our results show that there exists an open set of solutions approaching the de Sitter state at late times, consistent with the cosmic no-hair conjecture. On the other hand, solutions that approach the flat FL state at early times are special and admit a so-called isotropic initial singularity. For both classes of models the asymptotic expansion of the line element contains an arbitrary spatial metric at leading order, indicating asymptotic spatial inhomogeneity. We show, however, that in the asymptotic regimes this spatial inhomogeneity is significant only at super-horizon scales.

Spikes in the Mixmaster regime of G2 cosmologies

We produce numerical evidence that spikes in the mixmaster regime of

New explicit spike solutions—non-local component of the generalized Mixmaster attractor

{G}_{2}

Asymptotic silence-breaking singularities

cosmologies are transient and recurring, supporting the conjecture that the generalized mixmaster behavior is asymptotically nonlocal where spikes occur. Higher-order spike transitions are observed to split into separate first-order spike transitions.

COSMOLOGICAL MODELS FROM A DYNAMICAL SYSTEMS PERSPECTIVE

By applying a standard solution-generating transformation to an arbitrary vacuum Bianchi type II solution, one generates a new solution with spikes commonly observed in numerical simulations. It is conjectured that the spike solutions are part of the generalized Mixmaster attractor.

Anisotropic universes with isotropic cosmic microwave background radiation

We discuss three complementary aspects of scalar curvature singularities: asymptotic causal properties, asymptotic Ricci and Weyl curvature, and asymptotic spatial properties. We divide scalar curvature singularities into two classes: so-called asymptotically silent singularities and singularities that break asymptotic silence. The emphasis in this paper is on the latter class which has not been previously discussed. We illustrate the above aspects and concepts by describing the singularities of a number of representative explicit perfect fluid solutions.

Generating Matter Inhomogeneities in General Relativity

It is useful to study the space of all cosmological models from a dynamical systems perspective, that is, by formulating the Einstein field equations as a dynamical system using appropriately normalized variables. We will discuss various aspects of this work, the choices of normalization factor, multiple representations of models, the past attractor, nonlinear dynamics in close-to-Friedmann–Lemaitre models, Weyl curvature dominance, and numerical simulations.

Fluid observers and tilting cosmology

We show the existence of spatially homogeneous but anisotropic cosmological models whose cosmic microwave background temperature is exactly isotropic at one instant of time but whose rate of expansion is highly anisotropic. Although these models require fine-tuning, they nevertheless show that the observation of a highly isotropic cosmic microwave background temperature cannot alone be used to infer that the universe is close to a Friedmann–Lemaitre model since the time of last-scattering.