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

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.