论文标题
Kantowski-Sachs Quantum宇宙学中的隧道波函数
The tunneling wavefunction in Kantowski-Sachs quantum cosmology
论文作者
论文摘要
我们使用一种路径综合方法来研究量子宇宙学中的隧道波函数，并使用空间拓扑$ s^{1} \ times s^{2} $和正宇宙学常数（kantowski-sachs模型）。如果将$ s^1 $和$ s^2 $的初始比例因子设置为零，则波函数（半经典地）源于奇异性的宇宙。这可能被解释为表明$ s^1 \ times s^2 $宇宙不能以非单一的方式从任何东西中核定成核。在这里，我们探讨了Halliwell和Louko的另一种建议，即从该模型中的Nothing创建到将初始音量设置为零。我们发现，该提案的唯一可接受的版本是将$ s^1 $的半径固定到零，并以平滑闭合的条件（缺乏圆锥形奇异性）补充了这一点。最终的波函数预测了高各向异性的膨胀宇宙，但是在后期，该宇宙在局部成为局部各向同性。与DE Sitter模型不同，除非将高斯 - 邦网期限添加到动作中，否则总成核概率不会被指数抑制。
We use a path-integral approach to study the tunneling wave function in quantum cosmology with spatial topology $S^{1}\times S^{2}$ and positive cosmological constant (the Kantowski-Sachs model). If the initial scale factors of both $S^1$ and $S^2$ are set equal to zero, the wave function describes (semiclassically) a universe originating at a singularity. This may be interpreted as indicating that an $S^1\times S^2$ universe cannot nucleate out of nothing in a non-singular way. Here we explore an alternative suggestion by Halliwell and Louko that creation from nothing corresponds in this model to setting the initial volume to zero. We find that the only acceptable version of this proposal is to fix the radius of $S^1$ to zero, supplementing this with the condition of smooth closure (absence of a conical singularity). The resulting wave function predicts an inflating universe of high anisotropy, which however becomes locally isotropic at late times. Unlike the de Sitter model, the total nucleation probability is not exponentially suppressed, unless a Gauss-Bonnet term is added to the action.
