论文标题
现代宇宙学中的真空能量：弯曲空间中量子场理论的分析及其在宇宙学上的应用
Vacuum Energy in Modern Cosmology: an analysis of quantum field theory in curved spaces and its application to cosmological spacetimes
论文作者
论文摘要
在过去的几十年中，在我们对大型宇宙的了解中，见证了前所未有的进步。特别是，越来越精确的宇宙学观察使我们发现了一种“暗能”的形式，目前主要是宇宙的扩张。另一方面，标准宇宙学模型中的基本问题指向原始通货膨胀时期的可能性。这两个扩展阶段通常都应由具有与经典或量子场真空能量相似的能量形式支配的事实。同时，弯曲空间（QFTC）中的量子场理论已证明是一个丰富的框架，可以分析时空曲率相关但不太极端的方案中量子性质现象。特别是，它对量子真空的结构和动力学产生新的见解。在本文中，我们对QFTC的基本原理进行了彻底的阐述，并在宇宙学的空间中提出了一些应用。特别注意通过理想化的粒子探测器模型的粒子的经验概念，以及在扩展FLRW空位时创造粒子创造的现象。此外，我们开发了绝热的重新规范化程序，并使用它来计算这些空间中的重新归一化应力张量。对于De Sitter空间中的非互操作标量场，我们发现它采用宇宙学常数的形式，尽管仅在Planckian密度下才能找到具有定量的自洽值。我们还提出了一个简单的通货膨胀模型的结构，该模型是由自我互动的经典标量场驱动的，并展示了该领域的量化波动如何产生几乎规模不变的功率谱，就像CMB中当前观察到的那样。
The last decades have witnessed an unprecedented advancement in our knowledge of the large scale universe. In particular, increasingly accurate cosmological observations have allowed us to discover a form of "dark energy", which presently dominates the expansion of the universe. On the other hand, fundamental problems in the standard cosmological model point towards the possibility of a primordial inflationary period. Both these expansion phases have in common the fact that they should be governed by forms of energy with properties much similar to those of vacuum energy of classical or quantum fields. In the meanwhile, quantum field theory in curved spaces (QFTCS) has proved a rich framework to analyze phenomena of a quantum nature in regimes where spacetime curvature is relevant, but not too extreme; particularly, it yields novel insights on the structure and dynamics of quantum vacuum. In this dissertation, we make a thorough exposition of the fundamentals of QFTCS and present some of its applications in cosmological spacetimes. Particular attention is given to the construction of an empirical notion of particles through an idealized model of particle detectors, and to the phenomenon of particle creation in expanding FLRW spacetimes. Further, we develop the procedure of adiabatic renormalization, and use it to compute the renormalized stress tensor in these spacetimes. For a noninteracting scalar field in de Sitter spaces, we find that it takes the form of a cosmological constant, although a quantitatively self-consistent value with the background expansion can only be found at Planckian densities. We also present a construction of a simple inflationary model, driven by a self-interacting classical scalar field, and show how the quantized fluctuations of this field could give rise to a nearly scale-invariant power spectrum, like the one that is currently observed in the CMB.
