论文标题
对哈勃长度的近期宇宙反弹的量子分析
Quantum analysis of the recent cosmological bounce in the comoving Hubble length
论文作者
论文摘要
我们将从减速到加速扩张的转变作为连接空间的弹跳，并研究其量子宇宙学，知道反射以使量子效应脱颖而出是臭名昭著的。我们使用形式主义通过将自然常数降级为集成常数来获得时间变量，并专注于仅包含辐射和宇宙常数$λ$的玩具宇宙，以实现其简单性。我们发现，除了命令歧义的常规因素外，量子方程的顺序有歧义，导致了两种不同的理论：一秒钟，另一个一阶。在这两种情况下，都可以定义两个时间变量，共轭为$λ$，并为运动的辐射常数。我们对二阶理论几乎没有进展，但能够为一阶理论提供解决方案。它们表现出众所周知的“铃声”，从而使事件和反射波干扰，甚至在峰值波数据包中也导致概率分布的振荡。我们还详细检查了半经典近似值内的概率度量。接近弹跳，概率分布变为双峰，一个峰值在接近经典限制的轨迹之后，但哈勃参数略微向下移动，另一个峰值则以$ b $的值最低为$ b $。对效果的检查仍然更接近弹跳，在涉及物质和$λ$的更现实的模型中，对未来的工作进行了检查。
We formulate the transition from decelerated to accelerated expansion as a bounce in connection space and study its quantum cosmology, knowing that reflections are notorious for bringing quantum effects to the fore. We use a formalism for obtaining a time variable via the demotion of the constants of Nature to integration constants, and focus on a toy Universe containing only radiation and a cosmological constant $Λ$ for its simplicity. We find that, beside the usual factor ordering ambiguities, there is an ambiguity in the order of the quantum equation, leading to two distinct theories: one second, the other first order. In both cases two time variables may be defined, conjugate to $Λ$ and to the radiation constant of motion. We make little headway with the second-order theory, but are able to produce solutions to the first-order theory. They exhibit the well-known "ringing" whereby incident and reflected waves interfere, leading to oscillations in the probability distribution even for well-peaked wave packets. We also examine in detail the probability measure within the semiclassical approximation. Close to the bounce, the probability distribution becomes double-peaked, with one peak following a trajectory close to the classical limit but with a Hubble parameter slightly shifted downwards, and the other with a value of $b$ stuck at its minimum. An examination of the effects still closer to the bounce, and within a more realistic model involving matter and $Λ$, is left to future work.
