论文标题
使用功能重统计组来计算第一学期时间
Computing First-Passage Times with the Functional Renormalisation Group
论文作者
论文摘要
在通货膨胀期间，我们使用功能性重量级化组（FRG）技术来分析观众场（$σ$）的行为，以遵守过度阻尼的Langevin方程。我们简要回顾了如何使用FRG的衍生化扩展来获得有效的运动方程（EEOM）的单点和两点函数，并为三点函数得出EEOM。我们展示了如何计算数量，例如功率谱的幅度和FRG的光谱倾斜。我们明确地为具有多个屏障的潜力做到了这一点，并表明许多不同的电位将对光谱倾斜度提供相同的预测，这表明观察值对潜在的局部特征不可知。最后，我们使用EEOM来计算观众场的第一音阶时间（FPT）数量。单点和两点函数的EEOM足以准确预测$ \ weft \ langle \ mathcal {n} \ right \ rangle $的平均时间，可以在两个障碍之间传播具有障碍的两个字段值，以及该时间$δ\ Mathcal {n}^2 $。它还可以准确地解决$ρ（\ Mathcal {n}）$花费时间的完整PDF，预测正确的指数尾巴。这表明，将此分析扩展到加速器可以正确捕获产生原始黑洞的模型中预期的指数尾巴。
We use Functional Renormalisation Group (FRG) techniques to analyse the behaviour of a spectator field, $σ$, during inflation that obeys an overdamped Langevin equation. We briefly review how a derivative expansion of the FRG can be used to obtain Effective Equations of Motion (EEOM) for the one- and two-point function and derive the EEOM for the three-point function. We show how to compute quantities like the amplitude of the power spectrum and the spectral tilt from the FRG. We do this explicitly for a potential with multiple barriers and show that in general many different potentials will give identical predictions for the spectral tilt suggesting that observations are agnostic to localised features in the potential. Finally we use the EEOM to compute first-passage time (FPT) quantities for the spectator field. The EEOM for the one- and two-point function are enough to accurately predict the average time taken $\left\langle \mathcal{N}\right\rangle$ to travel between two field values with a barrier in between and the variation in that time $δ\mathcal{N}^2$. It can also accurately resolve the full PDF for time taken $ρ(\mathcal{N})$, predicting the correct exponential tail. This suggests that an extension of this analysis to the inflaton can correctly capture the exponential tail that is expected in models producing Primordial Black Holes.
