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arXiv 2009.02898hep-thastro-ph.COgr-qc
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宇宙光学定理

The Cosmological Optical Theorem

Harry Goodhew, Sadra Jazayeri, Enrico Pajer

备注：
37+19 pages, 4 figures
发表信息：
JCAP04(2021)021
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摘要：

时间演化的么正性，或者通俗地说概率守恒，是我们通过量子场论描述基本相互作用的核心。散射振幅的么正性的含义是很好理解的，例如通过光学定理和切割规则。相比之下，弯曲时空中的in-in耦合子和宇宙的相关波函数的含义，通过宇宙学调查测量，就不那么透明了。对于具有一般局域相互作用的de Sitter时空中任意质量的场，在de Sitter等距下不需要是不变的，我们证明了么正性意味着具有$ n $场的宇宙的波函数的系数$ ψ_{n} $之间的无限组关系，我们称之为宇宙光学定理。对于接触图，我们的结果决定了$ ψ_{n} $的解析结构，并强烈约束其形式。例如，具有奇数个共形耦合标量场和任意数量的无质量标量场的任何相关器必须为零。对于四点交换图，宇宙光学定理在$ ψ_{3} $和$ ψ_{4} $之间，或者等价地在双谱和三谱之间，给出了一个简单而有力的关系。作为对这种关系的检验，我们讨论了引力子交换和自相互作用引起的单场暴胀中的三谱。此外，我们提供了一个详细的推导的宇宙学标量的总能量极点和平坦空间振幅之间的关系。我们提供了类似的子图奇点公式。我们的研究结果构成了一个新的，强大的工具，引导宇宙学模型。

英文摘要：

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 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 $ ψ_{3} $ and $ ψ_{4} $, 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.

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