The Cosmological Optical Theorem
The Cosmological Optical Theorem
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DOI：
10.1088/1475-7516/2021/04/021
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发表时间：
2020-09
影响因子：
6.4
通讯作者：
H. Goodhew;Sadra Jazayeri;E. Pajer
中科院分区：
文献类型：
--
作者：
H. Goodhew;Sadra Jazayeri;E. Pajer
时间演化的统一性，或者俗称的概率守恒，是我们通过量子场论描述基本相互作用的核心。例如，通过光学定理和切割规则，可以很好地理解一元性对散射幅度的影响。相比之下，弯曲时空中的In-In相关器和宇宙的相关波函数(通过宇宙学调查测量)的含义要不那么透明。对于具有束-戴维斯真空和一般局域相互作用的De Sitter时空中任意质量的场，不需要在De Sitter等距下保持不变，我们证明了唯一性蕴含着具有n个场的宇宙波函数的系数ψn之间的无限组关系，我们称之为宇宙光学定理。对于接触图，我们的结果决定了ψn的解析结构，并强烈地约束了它的形式。例如，任何具有奇数个共形耦合标量场和任意个无质量标量场的相关器都必须为零。对于四点交换图，宇宙学光学定理给出了ψ3和ψ4之间的简单而强大的关系，或者相当于双谱和三谱之间的关系。作为对这一关系的明确检验，我们从引力子交换和自相互作用两个方面讨论了单场暴胀中的三谱。此外，我们还详细地推导了宇宙相关器的总能量极点与平坦空间振幅之间的关系。我们给出了子图奇点的类似公式。我们的结果构成了一个新的、强大的工具来引导宇宙相关器。
The unitarity of time evolution, or colloquially the conservation of probability, sits at the heart of our descriptions of fundamental interactions via quantum field theory. The implications of unitarity for scattering amplitudes are well understood, for example through the optical theorem and cutting rules. In contrast, the implications for in-in correlators in curved spacetime and the associated wavefunction of the universe, which are measured by cosmological surveys, are much less transparent. For fields of any mass in de Sitter spacetime with a Bunch-Davies vacuum and general local interactions, which need not be invariant under de Sitter isometries, we show that unitarity implies an infinite set of relations among the coefficients ψ n of the wavefunction of the universe with n fields, which we name Cosmological Optical Theorem. For contact diagrams, our result dictates the analytic structure of ψ n and strongly constrains its form. For example, any correlator with an odd number of conformally-coupled scalar fields and any number of massless scalar fields must vanish. For four-point exchange diagrams, the Cosmological Optical Theorem yields a simple and powerful relation between ψ3 and ψ4, or equivalently between the bispectrum and trispectrum. As explicit checks of this relation, we discuss the trispectrum in single-field inflation from graviton exchange and self-interactions. Moreover, we provide a detailed derivation of the relation between the total-energy pole of cosmological correlators and flat-space amplitudes. We provide analogous formulae for sub-diagram singularities. Our results constitute a new, powerful tool to bootstrap cosmological correlators.