论文标题
部分可观测时空混沌系统的无模型预测
Lorentzian Vacuum Transitions with a Generalized Uncertainty Principle
论文作者
论文摘要
使用Wentzel-Kramers-brillouin近似研究，研究了在重力存在下在标量场电位的最小值之间的真空过渡概率。首先，我们提出了一种通过半古典方法求解Wheeler-Dewitt方程来计算这些过渡概率的方法，以适用于包含平方术语以及在汉密尔顿约束中的线性术语和线性的术语的任何模型，以这种方式概括了先前的结果。然后，我们应用这种方法来计算具有正曲率和无效曲率的Friedmann-Lemaitre-Robertson-Walker指标以及Bianchi III度量指标时，当MinisuperSpace的坐标遵守标准的不确定性原理以及一般的不确定性原理时。在所有情况下，我们都会比较结果，并发现考虑一般不确定性原理的效果是，概率起初会增强，但衰减更快，因此当相应的量表因子足够大时，概率就会降低。我们还考虑了各向异性的效果，并将Bianchi III度量的结果与扁平的FLRW度量标准进行了比较，该指标与其各向同性限制相对应，并评论了先前工作的差异。
The vacuum transition probabilities between to minima of a scalar field potential in the presence of gravity are studied using the Wentzel-Kramers-Brillouin approximation. First we propose a method to compute these transition probabilities by solving the Wheeler-DeWitt equation in a semi-classical approach for any model of superspace that contains terms of squared as well as linear momenta in the Hamiltonian constraint generalizing in this way previous results. Then we apply this method to compute the transition probabilities for a Friedmann-Lemaitre-Robertson-Walker metric with positive and null curvature and for the Bianchi III metric when the coordinates of minisuperspace obey a Standard Uncertainty Principle and when a Generalized Uncertainty Principle is taken into account. In all cases we compare the results and found that the effect of considering a Generalized Uncertainty Principle is that the probability is enhanced at first but it decays faster so when the corresponding scale factor is big enough the probability is reduced. We also consider the effect of anisotropy and compare the result of the Bianchi III metric with the flat FLRW metric which corresponds to its isotropy limit and comment the differences with previous works.
