分布宇宙学量避免软奇点穿越佯谬
The paradox of soft singularity crossing avoided by distributional cosmological quantities
摘要：
一个充满反查伯金气体和尘埃物质混合物的平坦弗里德曼宇宙演化成未来的软奇点，尽管有无限的潮汐力，测地线仍然可以继续。在奇点中，反查伯金气体的压力发散，而其能量密度为零。然而，尘埃的能量密度并没有消失，哈勃参数也没有消失，这意味着如果它的演化是连续的，它将进一步膨胀。如果是这样，反查伯金气体的能量密度和压力将变得不明确，因此只允许收缩。巧合的是，在这个宇宙学模型中，宇宙必须同时膨胀和收缩。从分布意义上重新定义反Chaubergin气体可以避免这一悖论。然后哈勃参数可以被镜像到奇点处有一个跳跃，允许随后的收缩。通过这种修改，弗里德曼，Raychaudhuri和连续性方程的集合在奇点及其附近都得到了遵守。
英文摘要：
A flat Friedmann universe filled with a mixture of anti-Chaplygin gas and dust-like matter evolves into a future soft singularity, where despite infinite tidal forces the geodesics can be continued. In the singularity the pressure of the anti-Chaplygin gas diverges, while its energy density is zero. The dust energy density however does not vanish, neither does the Hubble parameter, which implies further expansion, if its evolution is to be continuous. If so, the energy density and the pressure of the anti-Chaplygin gas would become ill-defined, hence only a contraction would be allowed. Paradoxically, the universe in this cosmological model would have to expand and contract simultaneously. The paradox can be avoided by redefining the anti-Chaplygin gas in a distributional sense. Then the Hubble parameter could be mirrored to have a jump at the singularity, allowing for a subsequent contraction. With this modification the set of Friedmann, Raychaudhuri and continuity equations are all obeyed both at the singularity and in its vicinity.
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