近日，瑞士的SwissScientific科技的C. A.Trugenbergeru团队研究了有效德西特空间、量子行为和大尺度谱维度(3+1)，相关成果已于2023年3月24日在国际权威学术期刊《高能物理杂志》上发表。

该团队指出，洛伦兹德西特时空时空并非是基本的，而只是更基本的量子引力基态的有效描述。这个宇宙学基态是一个图形，在大尺度上表现为一个恒定负曲率的黎曼流形。他们将物质在这个平衡态附近的行为建模为在图形涨落的有效热环境中的布朗运动，由通用的时间参数驱动。

他们展示了负曲率如何动态诱导相对论坐标时间的渐进出现，和由正曲率“有效Lorentzian流形”等距组控制的主导弹道运动，即de Sitter时空：在正曲率中的自由落体在渐近意义下等效于在负曲率中的布朗运动的主导行为。负曲率的局部极限定理意味着这个“有效de Sitter时空”的大尺度谱维数是(3+1)，独立于它的微观拓扑维度。在这个有效描述中，渐进布朗运动的次主分量变成了在一个三维欧几里得流形上的薛定谔量子行为。

研究人员表示，德西特时空本质上是我们自己的宇宙，但在量子水平上存在问题。

附：英文原文

Title: Effective de Sitter space, quantum behaviour and large-scale spectral dimension (3+1)

Author: Trugenberger, C. A.

Issue&Volume: 2023-03-24

Abstract: De Sitter space-time, essentially our own universe, is plagued by problems at the quantum level. Here we propose that Lorentzian de Sitter space-time is not fundamental but constitutes only an effective description of a more fundamental quantum gravity ground state. This cosmological ground state is a graph, appearing on large scales as a Riemannian manifold of constant negative curvature. We model the behaviour of matter near this equilibrium state as Brownian motion in the effective thermal environment of graph fluctuations, driven by a universal time parameter. We show how negative curvature dynamically induces the asymptotic emergence of relativistic coordinate time and of leading ballistic motion governed by the isometry group of an “effective Lorentzian manifold” of opposite, positive curvature, i.e. de Sitter space-time: free fall in positive curvature is asymptotically equivalent to the leading behaviour of Brownian motion in negative curvature. The local limit theorem for negative curvature implies that the large-scale spectral dimension of this “effective de Sitter space-time” is (3+1) independently of its microscopic topological dimension. In the effective description, the sub-leading component of asymptotic Brownian motion becomes Schrdinger quantum behavior on a 3D Euclidean manifold.

DOI: 10.1007/JHEP03(2023)186

Source: https://link.springer.com/article/10.1007/JHEP03(2023)186