arXiv 2209.025152022-09hep-thastro-ph.COgr-qc

广义非局域类$R^2$暴胀

Generalized non-local $R^2$-like inflation

Alexey S. Koshelev, K. Sravan Kumar, Alexei A. Starobinsky

备注：: 37 pages, 3 figures, Discussions extended, typos corrected, matches with the version published in JHEP
发表信息：: JHEP 07(2023) 146
DOI：: 10.1007/JHEP07(2023)146

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AI总结：

该研究推导了容许R²暴胀解的最普遍非局域高曲率引力理论，得到了对应的暴胀预言，指出其破坏单场暴胀一致性关系，可通过未来CMB和引力波观测检验量子引力本质。

摘要：

$R^2$暴胀是广义相对论（GR）通过二次标量曲率扩展得到的理论，它引入了早期宇宙的准德西特膨胀，该膨胀由作为达朗贝尔算符本征模的里奇标量主导。本文中，我们推导了容许$R^2$暴胀解的最普遍引力理论，该理论最终被证明是广义相对论的高曲率非局域扩展。我们详细研究了该理论中的暴胀扰动，并分析了导致有质量标量（标量引力子）和无质量张量自由度的形状因子结构。我们认为该理论仅包含有限数量的自由参数，这些参数可通过宇宙学观测确定。我们推导了广义非局域类$R^2$暴胀的预言，得到标量谱指数$n_s\neq 1-\frac{2}{N}$，且张标比$r<0.036$可取任意小于该上限的值。在该理论中，张量谱指数可正可负$n_t\neq 0$，且著名的一致性关系$r = -8n_t$以非平凡的方式被破坏。我们还计算了张量谱指数的跑动，并讨论了区分该模型与几类标量场暴胀模型的观测意义。这些预言使我们能够在未来的宇宙微波背景（CMB）和引力波观测范围内探究量子引力的本质。最后，我们评述了广义非局域类$R^2$暴胀的特征无法被所谓的单场暴胀有效场论的既有概念所涵盖，以及我们必须如何重新定义开展暴胀宇宙学研究的方式。

英文摘要：

The $R^2$ inflation which is an extension of general relativity (GR) by quadratic scalar curvature introduces a quasi-de Sitter expansion of the early Universe governed by Ricci scalar being an eigenmode of d'Alembertian operator. In this paper, we derive a most general theory of gravity admitting $R^2$ inflationary solution which turned out to be higher curvature non-local extension of GR. We study in detail inflationary perturbations in this theory and analyse the structure of form-factors that leads to a massive scalar (scalaron) and massless tensor degrees of freedom. We argue that the theory contains only finite number of free parameters which can be fixed by cosmological observations. We derive predictions of our generalized non-local $R^2$-like inflation and obtain the scalar spectral index $n_s\approx 1-\frac{2}{N}$ and any value of the tensor-to-scalar ratio $r<0.036$. In this theory, tensor spectral index can be either positive or negative $n_t\lessgtr 0$ and the well-known consistency relation $r = -8n_t$ is violated in a non-trivial way. We also compute running of the tensor spectral index and discuss observational implications to distinguish this model from several classes of scalar field models of inflation. These predictions allow us to probe the nature of quantum gravity in the scope of future CMB and gravitational wave observations. Finally we comment on how the features of generalized non-local $R^2$-like inflation cannot be captured by established notions of the so-called effective field theory of single field inflation and how we must redefine the way we pursue inflationary cosmology.

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