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

Abstract

In this study, we investigate the numerical stability of the covariant Baumgarte--Shapiro--Shibata--Nakamura (cBSSN) formulation against the Friedmann--Lemaître--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.