量子隧穿与爱因斯坦-Æther量子宇宙学中经典时空的出现

中文摘要 AI 辅助

我们在爱因斯坦-Æther引力的框架内研究了一个量子宇宙学模型。该模型由一个正曲率的FLRW宇宙组成，其物质内容由无压尘埃描述，并存在一个正的宇宙学常数$\Lambda$。我们首先利用Schutz的变分形式进行经典哈密顿分析，构造相空间并推导尺度因子的动力学。值得注意的是，我们确定了导致暴胀膨胀的特定初始条件，这些条件直接来源于潜在的量子动力学。随后，我们按照Dirac形式对模型进行量子化，得到宇宙波函数的Wheeler-DeWitt方程。我们数值求解该方程，并利用WKB近似研究我们的结果，计算量子隧穿概率$TP_{WKB}$以及一个综合隧穿概率$TP_{int}$，来自量子力学多世界解释的尺度因子的期望值，以及相应的玻姆轨迹。最后，我们分析了这些隧穿概率如何受到理论基本参数（$\Lambda, \sigma, \beta$）和尘埃流体能量$E$变化的影响。我们的结果表明，在$\Lambda$、$\sigma$和流体能量$E$较大而$\beta$较小的参数区域中，宇宙量子诞生的概率更高。

英文摘要

We investigate a quantum cosmological model within the framework of Einstein-Æther gravity. The model consists of a positively curved FLRW Universe whose matter content is described by pressureless dust, in the presence of a positive cosmological constant $Λ$. We first perform a classical Hamiltonian analysis utilizing Schutz's variational formalism, constructing the phase space and deriving the dynamics of the scale factor. Notably, we identify specific initial conditions that lead to an inflationary expansion, which are extracted directly from the underlying quantum dynamics. Subsequently, we quantize the model following Dirac's formalism, obtaining the Wheeler-DeWitt equation for the wave function of the Universe. We solve this equation numerically and investigate our results using the WKB approximation to compute quantum tunneling probabilities $TP_{WKB}$ alongside an integrated tunneling probability $TP_{int}$, the expectation value of the scale factor coming from the many-worlds interpretation of quantum mechanics, and the corresponding Bohmian trajectories. Finally, we analyze how these tunneling probabilities are influenced by variations in the fundamental parameters of the theory ($Λ, σ, β$) and the energy of the dust fluid $E$. Our results indicate a higher probability for the quantum birth of the Universe in a parameter regime characterized by larger values of $Λ, σ$, and fluid energy $E$, together with a smaller value of $β$.

发表机构

• Universidade do Estado do Rio de Janeiro（里约热内卢州立大学）
• Universidade Federal de Juiz de Fora（茹伊斯迪福拉联邦大学）

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