We extend the formalism of stochastic inflation to the setup of non-attractor inflation with a sound speed $c_s$. We obtain the Langevin equations for the superhorizon perturbations and calculate the stochastic corrections to curvature perturbation power spectrum. It is shown that the fractional stochastic corrections in mean number of e-folds and power spectrum are at the order of power spectrum. We also calculate the boundary crossing and the first hitting probabilities in a hypothetical dS space with two boundaries in field space. Furthermore, the stochastic corrections in power spectrum in a setup akin to eternal inflation with large diffusion term are calculated.

中文翻译：

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随机非吸引子通货膨胀

我们将随机膨胀的形式主义扩展到具有声速 $c_s$ 的非吸引子膨胀的设置。我们获得超视距扰动的朗之万方程并计算曲率扰动功率谱的随机校正。结果表明，平均e折叠数和功率谱的分数随机校正处于功率谱的数量级。我们还计算了在场空间中有两个边界的假设 dS 空间中的边界交叉和第一次命中概率。此外，计算了类似于具有大扩散项的永恒膨胀的设置中功率谱的随机校正。