arXiv 2501.021192025-01hep-thastro-ph.COgr-qc

宇宙学关联函数的巨大平直空间极限

The Massive Flat Space Limit of Cosmological Correlators

Imperial College（帝国理工学院）

Sebastian Cespedes, Sadra Jazayeri

备注：: 46 pages plus appendices and 14 figures (acknowledgements and text updated in v3, no changes to the scientific results)
发表信息：: JHEP 07 (2025), 032
DOI：: 10.1007/JHEP07(2025)032

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AI总结：

提出一种新的巨大平直空间极限，通过双标度极限将带重内部线的宇宙学关联函数约化为平直空间中的截肢费曼图，并计算了重粒子对暴胀关联函数的单圈贡献，揭示了新的等边形状非高斯信号。

摘要：

由于宇宙学关联函数的尺度不变性，识别出有用的平直空间极限（其中它们可以用闵可夫斯基空间中的可观测量表示）并非易事。近年来，研究表明动量空间关联函数在解析延拓后，其运动学复平面中的特定奇点处编码了平直空间振幅。这种平直空间极限是无质量的，因为振幅对应于相关平直空间过程的紫外区域，其中内部传播子的质量有效为零。在本文中，我们引入了一种新的巨大平直空间（MFS）极限，其中对应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，使用双标度极限。在此极限中，作为独立变量的外部能量与传播子质量成反比地趋于零，而传播子质量趋于无穷大。我们提出了一个通用的约化公式，将这一极限下的图表示为平直空间中截肢的费曼图。我们的结果强调了巨大费曼积分的丰富结构与涉及重场交换的宇宙学关联函数性质之间的深刻联系。利用这个约化公式，我们计算了小声速区域中来自重粒子的暴胀关联函数的单圈贡献，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，无法通过向单场暴胀有效场论添加局部项来重现。相反，它们可以通过将规定的空间非局部算子纳入有效场论中来捕捉。

英文摘要：

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.

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