Effiicient estimation of higher-order correlation functions from Inflation.

该博士项目将通过精确计算暴胀模型的高阶相关函数来推进早期宇宙理论和观测宇宙学之间的对抗。本项目将利用为研究宇宙微波天空中的三点相关器（或双谱）而开创的可分离本征函数（“模态”）方法，利用量子场论“内-内”形式主义，将这一方法应用于暴胀期间扰动的动态演化。以可分离形式的精确双谱形状的有效计算便于非高斯统计的数据分析搜索。该方法将开发从简单的例子与单场通货膨胀到多个领域和周期性的通货膨胀模型，其中不同的非高斯信号是预期的。与观测数据集（如宇宙微波背景图和星系巡天）的直接比较将指导和限制对基础物理学中暴胀的理解。

The PhD project will advance the confrontation between early universe theory and observational cosmology by accurately calculating higher-order correlation functions from inflationary models. Using separable eigenfunction ("modal") methods pioneered for studying the three-point correlator (or bispectrum) in the cosmic microwave sky, this project will apply this methodology to the dynamical evolution of perturbations during inflation using the quantum field theory "in-in" formalism. The efficient calculation of precise bispectrum shapes in separable form is convenient for data analytic searches for non-Gaussian statistics. The methodology will be developed from simple examples with single-field inflation to multiple field and periodic inflation models where distinct non-Gaussian signals are anticipated. Direct comparison with observational data sets, such as cosmic microwave background maps and galaxy surveys, will guide and constrain the understanding of inflation in fundamental physics.