论文标题
WKB近似中Bianchi IX模型角的量子动力学
Quantum dynamics of the corner of the Bianchi IX model in WKB approximation
论文作者
论文摘要
在本文中,我们分析了与空间曲率诱导的微型曲线空间中的潜在术语相关的角区域内的Bianchi IX Univers Dynamics。该研究是在真空中进行的,并且在存在无质量标量场$ ϕ $和宇宙常数项$λ$的情况下完成。我们研究了WKB方案的动力学,在这些方案中,在半经典级别上处理了各向同性MISNER变量(体积)和两个各向异性变量之一(以及存在时的$ ϕ $),而其余各向异性的自由度,一个属于纯量子的自由度。量子动力学始终将其依赖于时间依赖的schröedinger方程之一减少,以具有依赖时间频率的谐波电势。真空盒以碰撞和扩展的宇宙的范围进行处理,而在$ ϕ $和$λ$的存在下的动态则以$ t \ rightarrow \ infty \ infty $进行了研究。在两种分析中,各向异性变量的量子动力学都与其概率密度的腐烂标准偏差有关,对应于抑制相关的量子各向异性。在真空案例中,角构型成为动力学和进化的吸引子,类似于taub宇宙学之一,在非单明性初始宇宙的极限中。这表明,如果Bianchi动力学进入了电势角,那么将去除初始奇异性并出现taub图片。当$ ϕ $出现时的情况很好地模拟了通货膨胀宇宙的开发阶段。在这里,我们表明经典和量子各向异性都被指数抑制,因此所得的动力学对应于各向同性封闭的Robertson-Walker几何形状。
In this paper we analyse the Bianchi IX Universe dynamics within the corner region associated to the potential term which the spatial curvature induces in the Minisuperspace. The study is done in the vacuum and in the presence of a massless scalar field $ϕ$ and a cosmological constant term $Λ$. We investigate the dynamics in terms of WKB scenario for which the isotropic Misner variables (the volume) and one of the two anisotropic ones (and $ϕ$ when present) are treated on a semi-classical level, while the remaining anisotropy degree of freedom, the one trapped in the corner, is described on a pure quantum level. The quantum dynamics always reduces to the one of a time-dependent Schröedinger equation for a harmonic potential with a time dependent frequency. The vacuum case is treated in the limits of a collpasing and an expanding Universe, while the dynamics in presence of $ϕ$ and $Λ$ is studied for $t \rightarrow \infty $. In both analysis the quantum dynamics of the anisotropy variable is associated to a decaying standard deviation of its probability density, corresponding to a suppression of the quantum anisotropy associated. In the vacuum case, the corner configuration becomes an attractor for the dynamics and the evolution resembles that one of a Taub cosmology in the limit of a non-singular initial Universe. This suggests that if the Bianchi dynamics enters enough the potential corner then the initial singularity is removed and a Taub picture emerges. The case when $ϕ$ is present well mimics the De-Sitter phase of an inflationary Universe. Here we show that both the classical and quantum anisotropies are exponentially suppressed, so that the resulting dynamics corresponds to an isotropic closed Robertson-Walker geometry.