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.

翻译：本研究探讨了协变Baumgarte--Shapiro--Shibata--Nakamura（cBSSN）表述在Friedmann--Lemaître--Robertson--Walker时空背景下的数值稳定性。为评估数值稳定性，我们通过约束演化方程的特征值分析计算了约束放大因子。为提高数值稳定性，我们提出了对cBSSN表述时间演化方程的修正方案。此外，我们采用修正后的表述进行数值模拟，以验证其稳定性的提升。