标题： 用微扰论重新审视随机膨胀理论 显示英文标题

标题： Revisiting stochastic inflation with perturbation theory

摘要： 长久以来，宇宙膨胀研究中的一个难题在于如何完全调和随机方法与微扰理论。 即使在最简单的单标量场情形下，该标量场的自相互作用由任意势决定且背景为固定的de Sitter空间时，这两种形式主义之间的完整联系依然难以捉摸。 利用微扰理论，我们计算了初始涨落的一点概率密度函数，并将其展开到势的第一阶。 我们探讨了在何种条件下我们的解满足随机方法中遇到的福克-普朗克方程。 我们识别出差异并阐明其根源，从而揭示了随机形式主义的状态。 显示英文摘要

摘要： A long-standing problem within the study of cosmic inflation consists in fully reconciling the stochastic approach with perturbation theory. A complete connection between both formalisms has remained elusive even in the simple case of a single scalar field with self-interactions determined by an arbitrary potential, in a fixed de Sitter background. Using perturbation theory, we compute the one-point probability density function for primordial fluctuations valid to first order in the potential. We examine under which conditions our solution respects the Fokker-Planck equation encountered within the stochastic approach. We identify discrepancies and elucidate their origins, allowing us to shed light on the status of the stochastic formalism.