FLRW小超空间中的随机时钟能否防止动力学奇点？
Can Stochastic Clocks in FLRW Minisuperspace Prevent Dynamical Singularities?
AI总结：
该研究在FLRW小超空间中扩展惠勒-德维特方程为随机形式，利用拉普拉斯-贝尔特拉米量子化等方法，证明半经典粗粒化产生的随机反作用可动态规避大爆炸奇点。
AI中文摘要：
我们在FLRW小超空间中发展了惠勒-德维特方程的随机扩展形式，证明量子反作用可动态调节大爆炸奇点，无需施加外部边界条件。利用拉普拉斯-贝尔特拉米量子化和粗粒化引力子模式的开放系统处理，我们得到随机哈密顿演化方程，其中扩散系数形式为σ(a)∝a²。该乘性噪声在原点处消失，使a=0成为费勒分类中的入口边界，导致拉普拉斯-贝尔特拉米加权稳态密度的超指数抑制，且无流入奇点的概率通量。在大尺度因子下，整体行为取决于宇宙学扇区：德西特和正势主导区域呈现幂律稳态尾，而束缚势或负有效宇宙学常数导致无穷远处的入口边界及全局可归一化稳态。综上，半经典粗粒化产生的随机反作用为小超空间量子宇宙学中的奇点规避提供了一致的动力学机制。
英文摘要：
We develop a stochastic extension of the Wheeler--DeWitt equation in FLRW minisuperspace and show that quantum backreaction can dynamically regulate the big bang singularity without imposing external boundary conditions. Using Laplace--Beltrami quantisation and an open-system treatment of coarse-grained graviton modes, we obtain a stochastic Hamiltonian evolution equation in which the diffusion coefficient takes the form $σ(a)\propto a^2$. This multiplicative noise vanishes at the origin and renders $a=0$ an entrance boundary in Feller's classification, leading to super-exponential suppression of the Laplace--Beltrami weighted stationary density and zero probability flux into the singular point. At large scale factor, the global behaviour depends on the cosmological sector: de Sitter and positive potential-dominated regimes exhibit power-law stationary tails, whereas confining potentials or negative effective cosmological constant lead to an entrance boundary at infinity and a globally normalizable steady state. Taken together, these results indicate that stochastic backreaction arising from semiclassical coarse-graining provides a consistent and dynamical mechanism for singularity avoidance in minisuperspace quantum cosmology.
