Effective Descriptions of Quantum Gravity and Cosmology

该项目的主要目的是完成规范语言中量子系统的有效描述的制定。特别是正则量子引力场（包括圈量子引力）需要比标准有效作用量更一般的设置，例如允许扩大的规范结构，一般协方差和相关的自由改变时间变量，以及非高斯或非真空状态作为扩展基础。与现有的公式相比，该项目中的工作提供的主要扩展将导致有效量子场论的规范版本。应用将包括正则量子引力的重整化分析，与有效量子引力的现有结果进行比较以检查圈量子引力的低能极限，以及早期宇宙的结构形成和初始状态的可能限制。量子引力预计在高能量密度下是重要的，例如在大爆炸期间或之后的早期宇宙。在这样的体系中，时空本身，而不仅仅是时空中的物质，被描述为受量子不确定性和涨落影响的波函数。由于一些概念和技术上的原因，很难评估这些波函数的潜在物理观测，但在粒子物理学中，它们的含义通常可以近似和使用有效方程推导。粒子物理学的标准方法不能直接应用于量子引力，在量子引力中，时空的经典结构不再存在。该项目旨在完成适用于量子引力的有效方程的设置，在此过程中，还将涉及几个数学兴趣问题（如泊松几何和代数结构）。它将为物理宇宙学提供新的场景和方程，包括量子引力效应的早期宇宙结构形成。

The main aim of this project is to complete the formulation of effective descriptions of quantum systems in canonical language. Especially the field of canonical quantum gravity (including loop quantum gravity) requires a more general setting than standard effective actions, allowing for instance for an enlarged gauge structure, general covariance and the associated freedom to change the time variable, and a non-Gaussian or non-vacuum state as expansion basis. Compared to existing formulations, the major extension provided by work in the project will lead to a canonical version of effective quantum field theory. Applications will include an analysis of renormalization in canonical quantum gravity, comparisons with existing results in effective quantum gravity to check the low-energy limit of loop quantum gravity, as well as structure formation in the early universe and possible restrictions on initial states.Quantum gravity is expected to be important at high energy density, for instance in the early universe during or just after the big-bang. In such regimes, space-time itself, and not just matter in space-time, is described by a wave function subject to quantum uncertainty and fluctuations. For several conceptual and technical reasons, it is difficult to evaluate such wave functions for potential physical observations, but as in particle physics, their implications can often be approximated and derived using effective equations. Standard methods of particle physics are not directly applicable to quantum gravity, in which the classical structure of space-time is no longer available. This project aims to complete the setting of effective equations suitable for quantum gravity, a process in which several questions of mathematical interest (such as Poisson geometry and algebraic structures) will be touched as well. It will contribute to physical cosmology by providing new scenarios and equations for structure formation in the early universe that include quantum-gravity effects.