arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 0910.3784gr-qc
收藏

极小时空尺度上的宇宙:量子几何动力学方法

Universe on Extremely Small Spacetime Scales: Quantum Geometrodynamical Approach

V. E. Kuzmichev, V. V. Kuzmichev

摘要:

量子几何动力学模型的半经典方法被用来描述宇宙在极小时空尺度上的性质。利用物质参考系作为宏观相对论性物质定义的动力学系统,在哈密顿形式的基础上建立了均匀、各向同性和封闭宇宙的量子理论。该模型的方程被简化为爱因斯坦型方程的形式,其中物质能量密度具有量子性质的两个分量,其表现为反引力流体。第一个分量在极限h -> 0时不为零,并且可以与暗能量相关联。第二个分量由非常严格的状态方程描述,并在过渡到大时空尺度后趋于零。在小的时空尺度上,这种量子修正决定了宇宙的几何形状。这种几何与嵌入在五维欧氏平坦空间中的单位四球共形。当到达后普朗克时代时,宇宙的几何变成在五维洛伦兹签名平坦空间中共形于单位四双曲面的几何。在两个区域之间的边界附近,宇宙几乎经历了指数膨胀,在辐射支配物质的作用下,宇宙平稳地进入膨胀,这是由标准宇宙学模型描述的。

英文摘要:

The semi-classical approach to the quantum geometrodynamical model is used for the description of the properties of the universe on extremely small spacetime scales. Quantum theory for a homogeneous, isotropic and closed universe is constructed on the basis of a Hamiltonian formalism with the use of material reference system as a dynamical system defined by macroscopic relativistic matter. The equations of the model are reduced to the form of the Einstein-type equations in which the matter energy density has two components of quantum nature, which behave as antigravitating fluids. The first component does not vanish in the limit h -> 0 and can be associated with dark energy. The second component is described by extremely rigid equation of state and goes to zero after the transition to large spacetime scales. On small spacetime scales this quantum correction determines the geometry of the universe. This geometry is conformal to a unit four-sphere embedded in a five-dimensional Euclidean flat space. When reaching the post-Planck era, the geometry of the universe changes into the geometry conformal to a unit four-hyperboloid in a five-dimensional Lorentz-signatured flat space. Near the boundary between two regions the universe undergoes almost an exponential expansion which passes smoothly into the expansion under the action of radiation dominating over matter which is described by the standard cosmological model.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑