标题： 宇宙关联函数的大平空间极限 显示英文标题

标题： The Massive Flat Space Limit of Cosmological Correlators

摘要： 识别宇宙相关函数中有用的平直空间极限是一项非平凡的任务，因为这些函数具有尺度不变的性质，并且可以用闵可夫斯基空间中的可观测量来表示。近年来，研究表明，在动量空间的相关函数中编码了特定奇点处的平直空间振幅，这些奇点出现在它们动力学复平面经过解析延拓后。这种平直空间极限是无质量的，意味着振幅对应于关联的平直空间过程的紫外区域，其中内部传播子的质量实际上为零。 本文提出了一种新的有质量的平直空间（MFS）极限，在此极限下，对应于平直空间费曼图中的内部质量保持有限。我们的提议适用于具有轻外部腿和重内部线的任意图，采用双尺度极限方法。在此极限下，将外能视为独立变量，它们以与传播子质量成反比的方式趋于零，而传播子质量则趋于无穷大。我们提出了一个通用的约化公式，该公式通过表达此极限下的图与平直空间中截断的费曼图来实现。我们的研究结果强调了有质量费曼积分的丰富结构与涉及重场交换的宇宙相关函数的特性之间的深刻联系。利用这一约化公式，我们在小声速区域计算了由重粒子对膨胀相关函数的一次圈贡献，揭示了新的双谱形状。我们发现的非高斯信号在等边配置附近尤为显著，无法通过向单场膨胀的有效场论添加局域项来再现。相反，它们可以通过将规定的空间非局域算符纳入EFT中来捕捉。 显示英文摘要

摘要： Identifying useful flat-space limits for cosmological correlators, where they can be expressed in terms of observables in Minkowski space is nontrivial due to their scale-invariant nature. In recent years, it has been shown that momentum-space correlators encode flat-space amplitudes at specific singularities that emerge in the complex plane of their kinematics after analytical continuation. This flat-space limit is massless in the sense that the amplitude corresponds to the ultraviolet regime of the associated flat-space process, where the masses of the internal propagators are effectively zero. In this paper, we introduce a novel massive flat-space (MFS) limit, in which the internal masses in the corresponding flat-space Feynman graph remain finite. Our proposal applies to arbitrary graphs with light external legs and heavy internal lines, using a double-scaling limit. In this limit, the external energies, treated as independent variables, approach zero in inverse proportion to the propagator masses, which are sent to infinity. We present a general reduction formula that expresses diagrams in this limit in terms of amputated Feynman graphs in flat space. Our findings underscore the deep connections between the rich structure of massive Feynman integrals and the properties of cosmological correlators involving the exchange of heavy fields. Using this reduction formula, we compute sample one-loop contributions from heavy particles to inflationary correlators in the small sound-speed regime, revealing novel bispectrum shapes. The non-Gaussian signals we uncover, which are especially pronounced around the equilateral configuration, cannot be reproduced by adding local terms to the effective field theory of single-field inflation. Instead, they are captured by incorporating prescribed spatially non-local operators into the EFT.