非局所理論とその宇宙論的意義

R2膨胀是广义相对论(GR)的二次标量曲率的推广，它引入了由Ricci标量支配的早期宇宙的准de Sitter展开，它是d‘Alembertian算符的本征模。他导出了一个允许R2膨胀解的最一般的引力理论，证明它是GR的高曲率非局部扩张。他详细研究了这一理论中的膨胀微扰，并分析了导致大质量标量(标量)和无质量张量自由度的形状因子的结构。他认为，该理论只包含有限数量的自由参数，这些参数可以通过宇宙学观测来确定。他得到了广义非定域类R2暴涨的预测，并得到了标量谱指数ns为1-2/N和张量与标量比r&lt；0.036的任意值。在这个理论中，张量谱指数可以是正的也可以是负的，并且以一种非平凡的方式打破了众所周知的一致性关系。他还计算了张量谱指数的运行，并讨论了观测意义，以将该模型与几类标量场膨胀模型区分开来。这些预测使我们能够在未来的CMB和引力波观测范围内探索量子引力的本质。

The R2 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. He derived a most general theory of gravity admitting R2 inflationary solution which turned out to be higher curvature non-local extension of GR. He studied in detail inflationary perturbations in this theory and analysed the structure of form factors that leads to a massive scalar (scalaron) and massless tensor degrees of freedom. He argued that the theory contains only finite number of free parameters which can be fixed by cosmological observations. He derived predictions of our generalized non-local R2-like inflation and obtain the scalar spectral index ns is 1 - 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 and the well-known consistency relation is violated in a non-trivial way. He also computed running of the tensor spectral index and discussed 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.