论文标题
关于通货膨胀率的过去完整
On the past-completeness of inflationary spacetimes
论文作者
论文摘要
我们讨论了一个问题，即在无限的过去是否可以在地球上完成通货膨胀的问题。大地完整性是在永恒通货膨胀期间避免初始奇异性的必要条件。经常认为，宇宙学模型的扩展足够快（具有平均哈勃扩展率$ h_ {avg}> 0 $）必须在null和Timelike过去的方向上不完整。这种众所周知的猜想依赖于过去定向的时间表或无效的大地测量的哈勃参数积分的特定边界。如前所述，我们表明这一主张是一个空旷的问题。我们表明，$ h_ {avg} $的计算对于基于基本拓扑假设的给定时空产生了一系列结果。我们提出了$ H_ {AVG} $的改进定义，并引入了无限的无限解决方案，尽管具有$ h_ {avg}> 0 $，但尽管有$ h_ {avg}> 0 $。我们讨论了通货膨胀间距以及对物理合理规模因素的量子（半古典）宇宙学问题的标准化定义。
We discuss the question of whether or not inflationary spacetimes can be geodesically complete in the infinite past. Geodesic completeness is a necessary condition for averting an initial singularity during eternal inflation. It is frequently argued that cosmological models which are expanding sufficiently fast (having average Hubble expansion rate $H_{avg}>0$) must be incomplete in null and timelike past directions. This well-known conjecture relies on specific bounds on the integral of the Hubble parameter over a past-directed timelike or null geodesic. As stated, we show this claim is an open issue. We show that the calculation of $H_{avg}$ yields a continuum of results for a given spacetime predicated upon the underlying topological assumptions. We present an improved definition for $H_{avg}$ and introduce an uncountably infinite cohort of cosmological solutions which are geodesically complete despite having $H_{avg}>0$. We discuss a standardized definition for inflationary spacetimes as well as quantum (semi-classical) cosmological concerns over physically reasonable scale factors.
