标题： 路径积分、鞍点和宇宙的开始 显示英文标题

标题： Path integrals, saddle points and the beginning of the universe

摘要： 在弯曲时空中的量子场论中理解早期宇宙，其中经典的背景时空通常是FLRW宇宙学，其上传播的量子场包括引力波和能量密度涨落。许多开放性问题似乎与我们对该领域了解甚少有关，其中一部分引力自由度被量子化，仅有一部分。在这项工作中，我们通过赋予背景宇宙和涨落量子特性来研究这一极限，然后专注于背景宇宙几乎经典行为的极限。量子化是在量子广义相对论框架中通过费曼路径积分实现的。我们研究了正和负宇宙常数情况下引力路径积分的鞍点近似，利用迷你超空间近似，重点研究了不同类边界条件的影响。我们的主要发现是，无论是无边界提议还是欧几里得反德西特空间中的黑洞，路径积分都需要用诺伊曼初始条件来定义。实际上，诺伊曼条件对于恢复合理的黑洞热力学和稳定无边界提议是必要的。同时，在这两种情况下，它都可以看作是对进入求和的几何体的正则性要求。需要诺伊曼条件意味着无边界波函数的解释与哈特尔和霍金最初的直觉非常不同，因为初始膨胀率是固定的，而不是其大小。我们的黑洞结果支持这种无边界提议的实现，其中正则性是首要要求，并允许在弯曲时空中的良好定义的QFT极限。 显示英文摘要

摘要： The very early universe is understood in terms of quantum field theories on curved spacetime, where the classical background spacetime is typically an FLRW cosmology and the quantum fields which propagate on it include gravitational waves and energy density fluctuations. Many open questions seem to relate to the fact that we very little understand this regime, where part of the gravitational degrees of freedom, and only part of them, are quantized. In this work we study this limit by assigning quantum properties both to the background universe and the fluctuations and then focusing on the limit where the background universe behaves nearly classically. The quantization is realized in the framework of quantum general relativity through Feymann's path integrals. We study the saddle point approximation of gravitational path integrals in the cases of a positive and a negative cosmological constant making use of the minisuperspace approximation focusing on the impact of different classes boundary conditions. Our main finding is that, both for the no boundary proposal and black holes in Euclidean anti-de Sitter space, the path integral needs to be defined with Neumann initial conditions. The Neumann condition is in fact necessary to recover sensible black holes thermodynamics and to stabilize the no boundary proposal. At the same time, it can be seen, in both cases, as a regularity requirement on the geometries entering the sum. The need for Neumann conditions implies that the interpretation of the no boundary wavefunction is very different from Hartle and Hawking's original intuition, since the initial expansion rate of the universe is fixed rather than its size. Our results for black holes stand in support of this implementation of the no boundary proposal, where regularity is the primary requirement and allows for a well-defined QFT in curved spacetime limit.