论文标题
通货膨胀宇宙学的冯·诺伊曼代数描述
Von Neumann algebra description of inflationary cosmology
论文作者
论文摘要
我们研究了通货膨胀准则（DS）空间的von Neumann代数描述。与完美的DS空间不同，准DS空间允许整个地平线的非零能量通量，可以通过静态时间翻译发生器的期望值来识别。此外，随着与静态时间翻译相关的DS等轴测图被自发断裂，时间的波动会累积，从而引起能量通量的波动。当通货膨胀期间由$（ε_hh）^{ - 1} $给出时，其中$ε_h$是测量哈勃半径的增加速率的缓慢滚动参数，能量通量及其波动在$ g \ \ f \ f \ 0 $ limit中的波动差异。考虑到能量通量的波动，并在观察者的能量中考虑到，我们认为通货膨胀的准DS空间由II型$ _ \ infty $代数描述。由于熵不是从上方界定的，因此这与II型$ _1 $描述的完美DS空间的描述不同，其中最大纠缠最大化熵。我们还表明，我们的结果与观察结果一致：反映上述波动的密度基质的von Neumann熵被解释为广义熵。
We study the von Neumann algebra description of the inflationary quasi-de Sitter (dS) space. Unlike perfect dS space, quasi-dS space allows the nonzero energy flux across the horizon, which can be identified with the expectation value of the static time translation generator. Moreover, as a dS isometry associated with the static time translation is spontaneously broken, the fluctuation in time is accumulated, which induces the fluctuation in the energy flux. When the inflationary period is given by $(ε_H H)^{-1}$ where $ε_H$ is the slow-roll parameter measuring the increasing rate of the Hubble radius, both the energy flux and its fluctuation diverge in the $G \to 0$ limit. Taking the fluctuation in the energy flux and that in the observer's energy into account, we argue that the inflationary quasi-dS space is described by Type II$_\infty$ algebra. As the entropy is not bounded from above, this is different from Type II$_1$ description of perfect dS space in which the entropy is maximized by the maximal entanglement. We also show that our result is consistent with the observation that the von Neumann entropy for the density matrix reflecting the fluctuations above is interpreted as the generalized entropy.
