标题： 全息宇宙学的新可观测量 显示英文标题

标题： A new observable for holographic cosmology

摘要： 双锥几何是引力路径积分的马鞍点，这解释了黑洞微观态谱的混沌统计特性。 这种几何通常是AdS-Schwarzschild黑洞，但时间坐标具有周期性识别；在黑洞视界处产生的奇点通过使几何略微复化来调节。 在这里，我们考虑双锥几何的推广，其中包括位于事件视界和黑洞奇点之间的洛伦兹宇宙学。 我们在二维和三维情况下分析了这种情况，其中宇宙学具有紧致的空间截面和大爆炸/大挤压奇点。 这些奇点以同样的方式通过略微复化度规来调节。 我们证明，在满足Kontsevich-Segal准则的情况下，这是可能的，这意味着这些几何可以被解释为广义相对论中的微扰稳定马鞍点。 这个过程导致了一种用对偶边界CFT中的标准可观测量描述宇宙学的新方法。 在三维情况下，宇宙学解为边界CFT中状态密度的两点函数提供了新的贡献。 与通常的双锥不同，它描述了不同质量的黑洞微观态之间的相关性，并在极限情况下描述了重态和接近BTZ阈值的态之间的统计相关性。 显示英文摘要

摘要： The double-cone geometry is a saddle of the gravitational path integral, which explains the chaotic statistics of the spectrum of black hole microstates. This geometry is the usual AdS-Schwarzschild black hole, but with a periodic identification of the time coordinate; the resulting singularity at the black hole horizon is regulated by making the geometry slightly complex. Here, we consider generalizations of the double-cone geometry which include the Lorentzian cosmology that sits between the event horizon and the black hole singularity. We analyze this in two and three dimensions, where the cosmology has compact spatial sections and big bang/crunch singularities. These singularities are regulated in the same way by slightly complexifying the metric. We show that this is possible while satisfying the Kontsevich-Segal criterion, implying that these geometries can be interpreted as perturbatively stable saddle points in general relativity. This procedure leads to a novel description of the cosmology in terms of standard observables in the dual boundary CFT. In three dimensions, the cosmological solution gives a new contribution to the two-point function of the density of states in the boundary CFT. Unlike the usual double cone, it describes correlations between black hole microstates with different masses, and in a limit describes correlations between the statistics of heavy states and states near the BTZ threshold.