叶状时空上的量子引力--渐近安全可靠
Quantum gravity on foliated spacetime - asymptotically safe and sound
摘要：
渐近安全提供了一种机制，用于构建一个在所有长度尺度上都有效的一致的和预测性的引力量子理论。它的关键成分是一个非高斯的引力重整化群流的不动点，它控制着耦合和关联函数在高能量下的标度。在这项工作中，我们使用的功能重整化群方程适用于ADM形式的宇宙学Friedmann-Robertson-Walker背景下的引力重整化群流评估。除了具有UV-非高斯渐近安全不动点特性外，该设置还具有第二个非高斯不动点，该不动点具有正牛顿常数和实临界指数。新的不动点改变了相图，使得所有与经典广义相对论相关的重整化群轨迹在所有长度尺度上都是明确的。特别是一个积极的宇宙学常数动态驱动到零，在深红外线。此外，与因果设置中出现的普适性类相关的标度维度与$ε$ -二维展开、基于格量子引力的蒙特卡罗模拟和离散化惠勒-德维特方程中的结果定性一致。
英文摘要：
Asymptotic Safety provides a mechanism for constructing a consistent and predictive quantum theory of gravity valid on all length scales. Its key ingredient is a non-Gaussian fixed point of the gravitational renormalization group flow which controls the scaling of couplings and correlation functions at high energy. In this work we use a functional renormalization group equation adapted to the ADM-formalism for evaluating the gravitational renormalization group flow on a cosmological Friedmann-Robertson-Walker background. Besides possessing the UV-non-Gaussian fixed point characteristic for Asymptotic Safety the setting exhibits a second non-Gaussian fixed point with a positive Newton's constant and real critical exponents. The new fixed point alters the phase diagram in such a way that all renormalization group trajectories connected to classical general relativity are well-defined on all length scales. In particular a positive cosmological constant is dynamically driven to zero in the deep infrared. Moreover, the scaling dimensions associated with the universality classes emerging within the causal setting exhibit qualitative agreement with results found within the $ε$-expansion around two dimensions, Monte Carlo simulations based on Lattice Quantum Gravity, and the discretized Wheeler-deWitt equation.
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