论文标题
宇宙学作为交叉产品
Cosmology as a Crossed Product
论文作者
论文摘要
我们建议一个新的概念框架，其中使用与本地操作员在DE Sitter静态贴片上与本地运营商代数相关的$ iii $因子的交叉产物的Hilbert空间表示量子的通货膨胀宇宙学和新出现的相结合时间中翻译自动形态。在这种正式的框架标量曲率波动中，由保形时间自动构成的发生器的量子方差引起的重力势确定。选择作为代表性，在交叉产物的希尔伯特空间中，每种模式的有效真空状态和保形时间，我们评估量子方差和诱导的标量曲率波动。这导致了通货膨胀参数（1-N_S）\ SIM 0.0318和ε\ SIM 0.0027的模型独立表征，与Planck实验结果非常吻合。在这种正式的框架中，通货膨胀扩大了原始DS扩展宇宙中可观察到的代数。在这种延长时间中，演变成为内部自动形态，共轭能量波动表现为可观察到的标量曲率波动。
We suggest a new conceptual frame where inflationary Cosmology is quantum mechanically described using the Hilbert space representation of the crossed product of the type $III$ factor associated with the algebra of local operators on the de Sitter static patch and the automorphism of translations in the emergent conformal time. In this formal framework scalar curvature fluctuations are determined by the gravitational potential induced by the quantum variance of the generator of the conformal time automorphisms. Choosing as representative, in the Hilbert space of the crossed product, the effective vacuum state for each mode and conformal time, we evaluate the quantum variance and the induced scalar curvature fluctuations. This leads to a model independent characterization of the inflationary parameters (1-n_s) \sim 0.0318 and ε\sim 0.0027 in good agreement with Planck experimental results. In this formal frame inflation extends the algebra of observables in a primordial dS expanding Universe. In this extension time evolution becomes an inner automorphism and the conjugated energy fluctuations manifest as the observable scalar curvature fluctuations.
