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arXiv 1810.04429gr-qc
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3+2宇宙学:统一FRW度量

3+2 Cosmology: unifying FRW metrics in the bulk

Carles Bona, Miguel Bezares, Bartolomé Pons-Rullan, Daniele Viganò

摘要:

宇宙学问题被认为是在一个五维(体)流形与两个时间坐标,服从真空爱因斯坦场方程。这里使用了演化形式主义,以便得到结果约束的简单形式。在空间平坦的情况下,这种方法允许找出一般的解决方案,这恰好是在一个单一的度量。所有嵌入的Friedmann-Robertson-Walker(FRW)度量都可以从这个“母”度量(“M-度量”)中获得,通过投影到不同的四维超曲面(膜)上。在本体中有一个时间平面允许设计出特定的曲线,该曲线将被保持为膜中的物理时间坐标。这种方法适用于确定FRW正规解,从无限的过去(没有大爆炸),即使有一个渐进的初始状态与非零半径(紧急宇宙)。明确的反例,显示不是每个空间平坦的FRW度量实际上可以嵌入在3+2散装流形。这意味着坎贝尔定理在广义相对论中的推广在这种情况下只适用于其较弱的形式,需要额外的假设,即约束方程至少在单个4D超曲面中成立。

英文摘要:

The Cosmological Problem is considered in a five-dimensional (bulk) manifold with two time coordinates, obeying vacuum Einstein field equations. The evolution formalism is used there, in order to get a simple form of the resulting constraints. In the spatially flat case, this approach allows to find out the general solution, which happens to consist in a single metric. All the embedded Friedmann-Robertson-Walker (FRW) metrics can be obtained from this 'mother' metric ('M-metric') in the bulk, by projecting onto different four-dimensional hypersurfaces (branes). Having a time plane in the bulk allows to devise the specific curve which will be kept as the physical time coordinate in the brane. This method is applied for identifying FRW regular solutions, evolving from the infinite past (no Big Bang), even with an asymptotic initial state with non-zero radius (emergent universes). Explicit counter-examples are provided, showing that not every spatially-flat FRW metric can actually be embedded in a 3+2 bulk manifold. This implies that the extension of the Campbell theorem to the General Relativity case works only in its weaker form in this case, requiring as an extra assumption that the constraint equations hold at least in a single 4D hypersurface.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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