arXiv 2103.086492021-03hep-thastro-ph.COgr-qc

从定域性和么正性到宇宙学关联函数

From Locality and Unitarity to Cosmological Correlators

Sadra Jazayeri, Enrico Pajer, David Stefanyszyn

备注：: Published version
DOI：: 10.1007/JHEP10(2021)065

摘要：

在推导暴胀预言的标准方法中，我们根据给定模型的规则在时间上演化出真空态。由于唯一的可观测量是关联函数的未来值，而不是它们的时间演化，这带来了很大的简并性：大量不同的模型被映射到相同的微小数量的可观测量。此外，由于缺乏时间平移不变性，即使是树级计算也需要越来越多的嵌套积分，这很快变得难以处理。在这里，我们要问有多少最终的观测量可以直接从局部性、么正性和对称性中“自举”出来。为此，我们引入了两个新的引导工具，以有效地计算宇宙学关联函数/波函数。第一个是显定域检验（MLT），无质量标量或引力子的任何$n$ -点（波）函数如果要从显定域理论产生，就必须满足这个检验。当与最近提出的Bootstrap规则的子集相结合时，这使我们能够显式地计算单个标量的导数中的所有阶数的所有双谱。由于我们没有引用软定理，这也可以扩展到多场暴胀。第二个是一个部分能量递归关系，使我们能够计算交换关联函数。结合Cauchy积分定理和宇宙光学定理的部分能量的一个定制的复杂的移位，我们固定交换关联函数的边界项。后者可以确定接触相互作用使用酉性和明显的局部性。作为一个例子，我们使用这些工具来引导标量暴胀三谱由于引力子交换和暴胀子自相互作用。

英文摘要：

In the standard approach to deriving inflationary predictions, we evolve a vacuum state in time according to the rules of a given model. Since the only observables are the future values of correlators and not their time evolution, this brings about a large degeneracy: a vast number of different models are mapped to the same minute number of observables. Furthermore, due to the lack of time-translation invariance, even tree-level calculations require an increasing number of nested integrals that quickly become intractable. Here we ask how much of the final observables can be "bootstrapped" directly from locality, unitarity and symmetries. To this end, we introduce two new bootstrap tools to efficiently compute cosmological correlators/wavefunctions. The first is a Manifestly Local Test (MLT) that any $n$-point (wave)function of massless scalars or gravitons must satisfy if it is to arise from a manifestly local theory. When combined with a sub-set of the recently proposed Bootstrap Rules, this allows us to compute explicitly all bispectra to all orders in derivatives for a single scalar. Since we don't invoke soft theorems, this can also be extended to multi-field inflation. The second is a partial energy recursion relation that allows us to compute exchange correlators. Combining a bespoke complex shift of the partial energies with Cauchy's integral theorem and the Cosmological Optical Theorem, we fix exchange correlators up to a boundary term. The latter can be determined up to contact interactions using unitarity and manifest locality. As an illustration, we use these tools to bootstrap scalar inflationary trispectra due to graviton exchange and inflaton self-interactions.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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