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arXiv 1209.5757hep-thgr-qc
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量子de Sitter的波函数

The Wave Function of Quantum de Sitter

Alejandra Castro, Alexander Maloney

摘要:

我们考虑了具有正宇宙学常数的三维量子广义相对论。Hartle-Hawking波函数被计算为在渐近未来无穷远处的度量数据的函数。从欧几里德Anti-de Sitter空间的解析延拓提供了度量空间中的自然积分轮廓,允许我们-在某些假设下-精确地计算波函数,包括微扰和非微扰效应。由此得到的波函数是未来无穷远的共形结构的一个不可归一化函数,它在I^+变得无限不均匀的几何中无限地达到峰值。我们解释这是一个非微扰的三维爱因斯坦引力德西特空间的不稳定性。

英文摘要:

We consider quantum general relativity in three dimensions with a positive cosmological constant. The Hartle-Hawking wave function is computed as a function of metric data at asymptotic future infinity. The analytic continuation from Euclidean Anti-de Sitter space provides a natural integration contour in the space of metrics, allowing us -- with certain assumptions -- to compute the wave function exactly, including both perturbative and non-perturbative effects. The resulting wave function is a non-normalizable function of the conformal structure of future infinity which is infinitely peaked at geometries where I^+ becomes infinitely inhomogeneous. We interpret this as a non-perturbative instability of de Sitter space in three dimensional Einstein gravity.

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