Stability analysis and improvement of the covariant BSSN formulation against the FLRW spacetime background

TL;DR

This paper analyzes the numerical stability of the covariant BSSN formulation in cosmological FLRW backgrounds and proposes modifications to enhance its stability, confirmed through eigenvalue analysis and numerical simulations.

Contribution

It introduces a modified cBSSN formulation with improved stability for simulations in FLRW spacetime, validated by eigenvalue analysis and numerical tests.

Findings

Eigenvalue analysis shows increased stability with the modification

Numerical simulations confirm improved stability of the modified formulation

Enhanced stability facilitates more reliable cosmological simulations

Abstract

In this study, we investigate the numerical stability of the covariant Baumgarte--Shapiro--Shibata--Nakamura (cBSSN) formulation against the Friedmann--Lema\^itre--Robertson--Walker spacetime. To evaluate the numerical stability, we calculate the constraint amplification factor by the eigenvalue analysis of the evolution of the constraint. We propose a modification to the time evolution equations of the cBSSN formulation for a higher numerical stability. Furthermore, we perform numerical simulations using the modified formulation to confirm its improved stability.