Stochastic dynamics during inflation

早期宇宙加速膨胀（暴胀）期间场的经典演化可以建立理想化的均匀和各向同性宇宙学，但量子涨落不可避免地在所有可观察尺度（及更高尺度）上产生不均匀性和各向异性。该项目将探索标量，矢量和张量场产生的波动的性质，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，以确定早期宇宙中存在的膨胀动力学和物理自由度。特别是，我们将探讨最近的发展，在随机方法来模拟通货膨胀的动力学，将量子场波动作为一个随机噪声。关于广义相对论中的随机方法和传统微扰方法之间的联系，包括长波（或分离宇宙）近似的使用，有一些重要的问题。我们还想更好地理解与最近量子场论结果的可能联系，例如软德西特有效理论。随机涨落可能对超高能物理敏感，因此考虑是否存在紫外线极限的观测结果（例如，幺正边界）是有趣的。最终，我们的目标是应用我们的结果来计算暴胀模型中原初场的全概率分布函数。该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.