AI 中文总结
该研究针对封闭宇宙波函数提出小喉部处方，通过在喉部施加边界条件的微型超空间路径积分描述半几何结构，引入小辐射分量模拟有限喉部，经特定条件限制和极限处理得到隧穿波函数，为宇宙创生研究提供新视角及方法。
AI 中文摘要
我们在洛伦兹路径积分形式体系中，为封闭宇宙的波函数提出了一种小喉部处方。宇宙创生可看作是通过小喉部与另一个宇宙相连的隧穿几何结构的解耦或夹断极限。我们通过在喉部施加边界条件的微型超空间路径积分来描述剩余的半几何结构，而非明确保留母宇宙一侧。在具有正宇宙学常数的封闭微型超空间模型中引入由\(\epsilon\)参数化的小辐射分量来模拟有限喉部。该辐射项产生两个转折点，内部的\(q_-\sim O(\epsilon)\)和外部的\(q_+\sim H^{-2}\)。我们的处方在初始端点施加诺伊曼条件\(\dot q(0)=0\)，并将初始大小\(q_i = q(0)\)限制在包含\(q_-\)的小喉部区域\(0<|q_i|<\sqrt{\epsilon}/H\)。取\(\epsilon\to0\)极限后，小喉部区域坍缩到\(q_i \to 0\)，鞍点作用量简化为标准隧穿鞍点的作用量。其他 lapse 轮廓选择可得到哈特尔 - 霍金型增长分支。从这个意义上说，隧穿波函数可作为洛伦兹路径积分中从任意小宇宙隧穿的极限形式得到，而非直接在消失几何处施加边界条件。
英文摘要
We propose a small-throat prescription for the wave function of a closed universe in the Lorentzian path integral formalism, motivated by the idea that universe creation may be obtained as the decoupling, or pinch-off, limit of a tunneling geometry connected to another universe through a small throat. Instead of retaining the parent-universe side explicitly, we describe the remaining half-geometry by a minisuperspace path integral with boundary conditions imposed at the throat. To model the finite throat, we introduce a small radiation component parametrized by $ε$ in a closed minisuperspace model with a positive cosmological constant. The radiation term produces two turning points, an inner one $q_-\sim O(ε)$ and an outer one $q_+\sim H^{-2}$, where $q$ is the square of the scale factor. Our prescription imposes the Neumann condition $\dot q(0)=0$ at the initial endpoint and restricts the initial size $q_i=q(0)$ to a small-throat domain $0<|q_i|<\sqrtε/H$ that contains $q_-$. This restriction selects the Riemann sheet containing the small-throat tunneling saddle and its Picard--Lefschetz cycle, while excluding the unsuppressed saddle associated with the outer turning point $q_+$. Taking the limit $ε\to0$ after this finite-throat saddle problem has been defined, the small-throat domain collapses to $q_i \to 0$, and the saddle action reduces to that of the standard tunneling saddle. Other choices of lapse contour can instead select Hartle--Hawking-type growing branches. In this sense, the tunneling wave function can be obtained as the limiting form of tunneling from an arbitrarily small universe in a Lorentzian path integral, rather than by imposing a boundary condition directly at a vanishing geometry.
Comments10 pages, 4 figures
