Inflationary Cosmology: Preparing the Theory to Match the Observations

在观测宇宙学最近和即将取得的进展的推动下，该研究项目将为研究现实的暴胀模型提供必要的理论框架，这些模型可以通过大量可用数据进行测试。具体来说，它将集中在预测曲率扰动中潜在的可检测的非高斯性水平以及可观测的引力波背景的场景上。考虑到与早期宇宙相关的高能量尺度，在高维统一场论（如弦/ m理论）的背景下发展暴胀情景是很自然的。我们将研究暴胀模型，其中我们可观测宇宙的加速膨胀是由于一个或多个“膜”的运动而产生的，这些“膜”沿着更高维度的弯曲喉形几何传播。本文将提出一种解析形式，用以解释由等曲率模态引起的绝热曲率扰动的演化。这将用于计算曲率摄动的三点和四点相关函数。我们将研究产生的任何非高斯性的水平和尺度依赖性如何取决于假设的初始真空状态的性质。我们将推导可观测参数之间的一致性方程，原则上可以用来排除或确认不同的暴胀模型。这提供了在任何形式的地球实验都无法达到的能量尺度上直接限制宇宙物理学的可能性，并将产生关于宇宙起源、演化和大尺度结构的独特信息。

Motivated by recent and forthcoming advances in observational cosmology, this program of research will develop the theoretical framework necessary for studying realistic inflationary models that can be tested against the wealth of available data. Specifically, it will focus on scenarios that predict potentially detectable levels of non-Gaussianity in the curvature perturbation as well as an observable gravitational wave background. Given the high energy scales associated with the very early universe, it is natural to develop inflationary scenarios within the context of higher-dimensional, unified field theories such as string/M-theory. We will study models of inflation where the accelerated expansion of our observable universe arises due to the motion of one or more `branes' propagating down a warped throat geometry of the higher dimensions. An analytical formalism will be developed that can account for the evolution of the adiabatic curvature perturbation due to isocurvature modes. This will be employed to calculate the three- and four-point correlation functions of the curvature perturbation. We will investigate how the level and scale-dependence of any non-Gaussianity that is generated depends on the nature of the initial vacuum state that is assumed. We will derive consistency equations between observable parameters that in principle could be employed to rule out or confirm different inflationary models. This offers the possibility of directly constraining the physics of the universe at energy scales that are inaccessible to any form of terrestrial experiment and will yield unique information on the origin, evolution and large-scale structure of the universe.