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.

时间演化的单一性，或者通俗地讲概率守恒，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，可以很好地理解幺正性对散射幅度的影响。相比之下，通过宇宙学调查测量的弯曲时空内相关器和相关宇宙波函数的含义要透明得多。对于在德西特时空具有 Bunch-Davies 真空和一般局部相互作用的任何质量的场，在德西特等距下不必保持不变，我们表明单一性意味着系数 ψ _n之间的无限关系 具有 n 个场的宇宙波函数，我们将其命名为宇宙光学定理。对于接触图，我们的结果决定了 ψ _n的解析结构并严格限制了它的形式。例如，任何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相关器都必须消失。对于四点交换图，宇宙光学定理在 ψ ₃和 ψ ₄之间产生了一个简单而强大的关系 ，或等效于双谱和三谱之间。作为对这种关系的明确检查，我们讨论了来自引力子交换和自相互作用的单场暴胀中的三谱。此外，我们提供了宇宙相关器的总能量极点与平坦空间振幅之间关系的详细推导。我们为子图奇异点提供了类似的公式。我们的结果构成了一个新的、强大的工具来引导宇宙学相关器。