Fully relativistic nonlinear cosmological evolution in spherical symmetry using the BSSN formalism

TL;DR

This paper introduces a fully relativistic numerical method using the BSSN formalism to simulate nonlinear cosmological evolution in spherical symmetry, enabling detailed studies of structure formation beyond linear approximations.

Contribution

It develops a novel numerical approach for relativistic cosmological simulations on a dynamical background, including handling of boundary conditions and stability analysis.

Findings

Successfully reproduces Lemaître-Tolman-Bondi solutions

Demonstrates stability and convergence of the method

Handles dynamical backgrounds and gauge dynamics

Abstract

We present a fully relativistic numerical method for the study of cosmological problems using the Baumgarte-Shapiro-Shibata-Nakamura formalism on a dynamical Friedmann-Lema\^itre-Robertson-Walker background. This has many potential applications including the study of the growth of structures beyond the linear regime. We present one such application by reproducing the Lema\^itre-Tolman-Bondi solution for the collapse of pressureless matter with arbitrary lapse function. The regular and smooth numerical solution at the center of coordinates proceeds in a natural way by relying on the Partially Implicit Runge-Kutta algorithm described in Montero and Cordero-Carri\'on [arXiv:1211.5930]. We generalize the usual radiative outer boundary condition to the case of a dynamical background and show the stability and convergence properties of the method in the study of pure gauge dynamics on a de Sitter background.