论文标题
封闭的弗里德曼宇宙的扰动和线性化稳定性
Perturbations and Linearization Stability of Closed Friedmann Universes
论文作者
论文摘要
我们考虑封闭的弗里德曼宇宙的扰动。通常已知两个最低的波数（$ l = 0 $和$ 1 $）的摄动模式是虚构的，但是在这里我们表明两者都是物理的。在爱因斯坦静态宇宙中，封闭的背景空间具有类似时间的杀伤向量，随之而来的是线性化不稳定性的问题。线性化方程的适当解决方案需要满足一阶变量二次组合的taub约束。我们在两个可用的基本规格条件下评估了taub约束，并表明在两个仪表中，$ l \ geq 1 $模式应伴随$ l = 0 $（同质）模式，以消失声速，$ c_ {s} $。对于$ c_ {s}^{2}> 1/5 $（标量字段支持的爱因斯坦静态模型属于这种情况，$ c_s^2 = 1 $），已知$ l \ geq 2 $模式是稳定的。为了在早期宇宙中，通货膨胀之前，没有奇异性，在早期宇宙中拥有稳定的爱因斯坦静态进化阶段，尽管taub约束并不禁止它，我们需要找到一种机制来抑制不稳定的$ l = 0 $和$ l = 1 $模式。
We consider perturbations of closed Friedmann universes. Perturbation modes of two lowest wavenumbers ($L=0$ and $1$) are generally known to be fictitious, but here we show that both are physical. The issue is more subtle in Einstein static universes where closed background space has a time-like Killing vector with the consequent occurrence of linearization instability. Proper solutions of the linearized equation need to satisfy the Taub constraint on a quadratic combination of first-order variables. We evaluate the Taub constraint in the two available fundamental gauge conditions, and show that in both gauges the $L\geq 1$ modes should accompany the $L=0$ (homogeneous) mode for vanishing sound speed, $c_{s}$. For $c_{s}^{2}>1/5$ (a scalar field supported Einstein static model belongs to this case with $c_s^2 = 1$), the $L\geq 2$ modes are known to be stable. In order to have a stable Einstein static evolutionary stage in the early universe, before inflation and without singularity, although the Taub constraint does not forbid it, we need to find a mechanism to suppress the unstable $L=0$ and $L=1$ modes.
