Numerical Investigation of Cosmological Singularities

TL;DR

This paper develops a numerical approach using symplectic PDE solvers to investigate the nature of cosmological singularities, specifically testing the BKL conjecture across models of increasing complexity.

Contribution

It introduces a symplectic PDE solver application to analyze the BKL conjecture in various cosmological models, including homogeneous and inhomogeneous universes.

Findings

Symplectic solver performs well compared to Runge-Kutta in homogeneous models

Demonstrates local Mixmaster dynamics in inhomogeneous cosmologies

Provides numerical evidence supporting the BKL conjecture

Abstract

We describe a numerical approach to address the BKL conjecture that the generic cosmological singularity is locally Mixmaster-like. We consider application of a symplectic PDE solver to three models of increasing complexity--spatially homogeneous (vacuum) Mixmaster cosmologies where we compare the symplectic ODE solver to a Runge-Kutta one, the (plane symmetric, vacuum) Gowdy universe on $T^3 \times R$ whose dynamical degrees of freedom satisfy nonlinearly coupled PDE's in one spatial dimension and time, and U(1) symmetric, vacuum cosmologies on $T^3 \times R$ which are the simplest spatially inhomogeneous universes in which local Mixmaster dynamics is allowed.