GR Dynamics of Stochastic Inflation

该博士项目将通过将随机暴胀方法与完全非线性广义相对论进化相结合，从暴胀模型中进行定量统计预测，推进早期宇宙暴胀理论，该理论解释了宇宙中星系和大尺度结构的起源。由于广义相对论和驱动暴胀的潜在因素可能相互作用所产生的非线性，非高斯特征固有地存在于原始波动中。该项目的目标是对非线性暴胀动力学进行分析和数值模拟，以便进行双谱（三点）和其他高阶相关器预测，这些预测涵盖了更广泛的暴胀情景（包括具有多个场的暴胀情景）；这是相互竞争的膨胀模型之间的一个重要区别，可以用来在观测上区分它们。这将通过利用新的GRChombo数值相对论管道来实现，利用全三维广义相对论模拟来计算这些非线性效应，并通过包含在膨胀期间被放大的量子波动来增强它。后者将作为随机源项实现，集成在GRChombo演化例程中，而后者将通过有效场论的微扰分析计算来确定。由博士生导师Shellard领导的DAMTP宇宙学家已经能够通过使用创新的可分离技术（MODAL管道）从宇宙微波背景（CMB）的普朗克卫星图中提取和重建温度和极化双光谱，从而限制大范围的暴胀情景；这一方法现在正被应用于来自CMB实验（西蒙斯天文台）和星系调查（SDSS、DES等）的新观测数据集。从这个博士项目得到的随机非线性GR模拟的三维场将直接适用于这些技术的分析，推进暴胀理论与宇宙数据的详细对抗

This PhD project will advance the early universe theory of inflation, which explains the origin of galaxies and large-scale structure in the Universe, by merging stochastic inflation methods with fully nonlinear General relativistic evolution to make quantitative statistical predictions from inflationary models. Non-Gaussian signatures are inherently present in primordial fluctuations due to the nonlinearities produced by both general relativity and the fact that the potential responsible for driving inflation may be interacting. The goal of this project is to analytically and numerically model nonlinear inflationary dynamics in order to make bispectrum (three-point) and other higher-order correlator predictions which encompass a much broader range of inflationary scenarios (including those with multiple fields); this is an important discriminant between competing inflation models that can be used to distinguish them observationally. This will be achieved by exploiting the new GRChombo numerical relativity pipeline to compute these nonlinear effects using full 3D general relativistic simulations, augmenting it by the inclusion of quantum fluctuations that get amplified during Inflation. The latter will be implemented as stochastic source terms to be integrated within the GRChombo evolution routines and which, in turn, will be determined via perturbative analytic computations from effective field theory. DAMTP cosmologists, led by the PhD supervisor Shellard, have been able to constrain a wide range of inflationary scenarios by using innovative separable techniques (the MODAL pipeline) to extract and reconstruct the temperature and polarization bispectra from Planck satellite maps of the cosmic microwave background (CMB); this is now being applied to new observational data sets from both CMB experiments (Simons Observatory) and galaxy surveys (SDSS, DES and beyond). The resulting 3D fields of the stochastic nonlinear GR simulations from this PhD project will be directly amenable to analysis by these techniques, advancing the detailed confrontation of inflationary theory with cosmological data