Stochastic dynamics during inflation

在宇宙早期的加速膨胀时期(膨胀)，场的经典演化可以建立理想化的均匀和各向同性的宇宙学，但量子涨落不可避免地在所有可观察的尺度上(甚至更远)产生不均匀和各向异性。这个项目将探索在标量场、矢量场和张量场中产生的涨落的本质，包括原始密度场和引力波，以及我们如何将这些预测与当前和未来的观测进行比较，以确定非常早期的宇宙中存在的膨胀动力学和物理自由度。特别是，我们将探索随机方法建模通货膨胀动力学的最新进展，将量子场波动合并为随机噪声。在广义相对论中，关于随机方法和传统微扰方法之间的联系有一些重要的问题，包括使用长波(或分离的宇宙)近似。我们还想更好地理解与最近的量子场理论结果的可能联系，例如软德西特有效理论。随机涨落可能对超高能物理很敏感，因此考虑是否存在紫外线极限的观测结果是很有趣的，例如，么正边界。最终，我们的目标是应用我们的结果来描述膨胀模型中原始场的全概率分布函数。这个项目涉及分析和数值工作的结合。

The classical evolution of fields during a period of accelerated expansion in the very early universe (inflation) can establish an idealised homogeneous and isotropic cosmology, but quantum fluctuations inevitably generate inhomogeneities and anisotropies on all observable scales (and beyond). This project will explore the nature of the fluctuations produced in scalar, vector and tensor fields, including the primordial density field and gravitational waves, and how we may compare these predictions against current and future observations to identify the inflationary dynamics and physical degrees of freedom present in the very early universe. In particular we will explore recent developments in the stochastic approach to modelling inflationary dynamics, incorporating quantum field fluctuations as a stochastic noise. There are important questions about the connection between the stochastic approach and traditional perturbative approaches in general relativity, including the use of the long-wavelength (or separate universe) approximation. We also want to understand better possible connections to recent quantum field theory results, such as soft de Sitter effective theory. Stochastic fluctuations can be sensitive to ultra-high energy physics so it is interesting to consider if there are observational consequences of the ultra- violet limit, for example, unitary bounds. Ultimately our aim is to apply our results to characterise the full probability distribution function for the primordial fields in inflationary models. This project involves a combination of analytic and numerical work.